Andy,

You discount my .458" experience and experiments which compare the 500gr Woodleigh Vs, the 450gr North Fork with the NF winnning penetration by near two to one.

JPK

/

JPK,

I do not discount your experience with the FN vs RN at all.

I completely agree!

My 450 grain NF-FN penetrated over 60 inches of elephant head three times.



My 465 grain TCCI/A-Square RN penetrated 33 and 39 inches in the same elephant.



Water tanks showed 39 inches to 120 inches for RN vs FN. Water tanks correlate very closely to unstable RN but not at all to FN.

(Alf, if a blunt RN like the A-square, with its center of gravity very near its center of form super cavitates why did it exit the water tanks sideways at less than a meter penetration?)



JPK, we agree, in the real world a non-deforming FN has almost a 2:1 advantage.



As I have said in the past, the only suitable test medium for an elephant skull is a dead elephant!



Anyone who has a theory they would like to prove is welcome to join me in Zimbabwe to prove or disprove it!

Cost of admission, three elephant.

Andy

quote:

Originally posted by Andy:
Jeffe,

You are trying to stir up trouble where there is none.

You forgot the part about where I said, "The La Grange stop box is a complete failure for FN bullets."

Do not mis-quote me by omission!

Unlike some here, I have an open mind. If an artificial test medium does not correlate to emperical results, I go back to the hunting fields.

So should you.

Andy

Andy,
I asked a valid question and you fly off the handle. calm down, think, and tell me again about that open minded position again?

Dan says NONE you say RNs..

THAT is the question at hand.

Does plywood work AT ALL or is it all bollocks?
It's a pretty straight forward question, and, if you operated from that vaulted open mind, you wouldn't have any issue answering that.

Perhaps, (openminded reference again) I was asking to determine the actual bullets to be used in my test. You don't mind if your results are vetted, do you?

If experimental media doesn't show field conditions, then you change the media to make a valid test. It's really pretty simple.

However, if test media does not yeild REPEATABLE results (not tends) the test is flawed. No matter what media.

Do you mind actually having a discussion, rather than a reaction?

quote:

Originally posted by Andy:
As I have said in the past, the only suitable test medium for an elephant skull is a dead elephant!

Andy

Thanks, this may be the fundimental break down in communication. Simulation of an elephants shull does not enter into my quest for information.

You see, if one presents the point that ABC test is only valid in an elephant's skull, it begs the question "what happens in a buffalo's body"... which is a meaningless distractor. I am interesting in how a bullet penetrates in a test media under given conditions, then modifying those conditions to have results, in an independantly verifiable media.

period.

How that relates to an elephants head, a buffalo's body, or a hippo's tailbone is field work, not baseline work.

all that being said, didn't you say

quote:

The La Grange stop box actually does predict penetration in elephant skulls very closely. . . for FMJ RN bullets!

Great, let's agree on this, and move on.

Now, The question is to Dan... do you agree that The La Grange stop box actually does predict penetration in elephant skulls very closely. . . for FMJ RN bullets! ?

All,
I am not trying to open a can of worms here, rather ask a simple question and move on. I haven't brought up elephants, twist, or motive...

Trying to ask a simple question to determine if we can all agree when test media trends to field results.


my last post in this thread.

Jeffe,

You said:

"Simulation of an elephants skull does not enter into my quest for information."

That is the only reason I was testing FMJ RN bullets, and later monolithic RN and FN.

I was going elephant hunting!

Andy

Hallo Andy,

what is a "La Grange stop box"?

I never shot an elphant and there for lack Information on the Skull structure. If I had that, I would be glad.




Namutomi Skull



Sectioned Skull

What i would really like to know is how much Bone must be penetrated for the frontal Brain shot. I mean not the hollows in the Comb structure, but the actual bone. If that would be known, i believe an artificial Replacement could be built to standardise Bullet proofing. Of Course You are rigt to say, only an Elefant is an Elefant, but i would rather "play" with a Substitute and optimize towards my Findings, before I shoot the real one.

Lutz

If you want to know which bullet is best ask Saeed,he'll tell you! When it comes to bullets Saeed is a Master!

Lutz,

I am not qualified to tell you about the depth of the elephant skull as I have only shot one.

But Will, 500 grains, Norbert, and many others here are.

Hopefully one of them will advise you.

Norbert told me some time ago that 60 inches front on and 48 inches sideways would be about correct. But I would rather these gentlemen advise you themselves.

A La Grange stop box is a series of more than 70 3/4 inch thick plywood boards, one foot square with a 3/4 inch space between them, developed by Mike La Grange of the Zimbabwe park department. He has killed over 1,000 elephants and found the results with FMJ-RN and monolithic solid bullets to closely correlate to his actual hunting experiences.

I made a similar stop box, and it correlates reasonably closely for RN bullets but not FN. There fore my statement that only a dead elephant (as 500 grains has demonstrated) was appropriate.

By "electrolytic" copper alloy do you mean what we call C110? This is one of the harder "pure" (99%) copper alloys but would probably split if used in a monolithic HP or bonded soft point bullet.

Andy

LutzM!

The amount of bone you have to penetrate to reach the brain on a frontal shot is dependent on the size and sex of the elephant but more importantly on how the elephant is holding it's head. When they charge they typicaly hold their heads very low so to reach the brain you must pace your bullet well above the eyeline, maybe as much as 8 inches higher. The advantage you have is that you are shooting at the top of the brain and in that position the surface area presented is quite large. The difficulty is that the head is bouncing as the feet hit the ground giving you a moving target. I would guess that in this case 24" of penetration will reach the brain and pass through it. If the elephant is facing you and feeding or not looking at you the head is then held higher and your aim point is somewhere close to the eye line maybe slightly above or slightly below depending on head height. In this case 30 to 40 inches penetration should carry the bullet through the brain. The most difficult frontal shot is when the elephant is standing looking down his nose at you, esp. if it is up hill from you. The big problem her is that the hard palate (the bone between the tusk sockets) is not parallel to your bullet entry and the bullet must now pass through and along the bone on it's line to the brain. I hit one elephant a full 8" (if memory serves me right) on the trunk below where the tusks come out of the lip for the correct height. Here is where you need maximum penetration. At least 48" in my estimation. I also think that this is a shot to avoid as the elephant is undisturbed and sooner or later will turn sideways and present a side brain or heart/lung shot.

465H&H

Hi Andy,

I do not know C110, but electrolytical Copper is 100% Copper, so it's pure.

I sometimes use 99% Copper with some Add-on. Such tiny Quantities of Something can make quite Difference. You notice, i hesitate to outline the 1%. I have been copied too often, to bee in the Mood, to make it too easy.



Competitor`s Splitter 2



Competitor`s Splitter 1

I have observed such Splits, but a Correlation to the Material seems not to exist. Maybe it does. I believe, but do not know for sure, the Pressing has some Influence.

LutzM

Hi 465H&H,

regarding Elephant head penetration, You write about XYZ Inches Penetration. Which Material or Method do You actually mean? Maybe the La Grange stop box, that Andy described? Maybe something else?

I would like to know, how much real BONE has to be penetrated, preferably in the three Directions that You described. I assume, but do not know, the hard Bone to penetrate varies between 4 - 6 or 8 Inches. Could someone experienced Elephant hunter please let me know this, or these Numbers?

Asks LutzM

Lutz,

I believe that 465 is an experienced elephant hunter and his descriptions are for elephant skull not a simulant.

I think you will find it very difficult to simulate an elephant skull. It is a complex object, thick hide, muscle, solid bone, bone with air space, and blood.

Andy

LutzM!

My appologies for not being more clear in my descriptions posted above. The measurement guestimates were based on total penetration from the outside the the skin through the brain.

I was trying to get accross to you how much variation there is in the amount of bone needed to be penetrated for various angles, ages, sex etc. I suspect very few bullets penetrate the same number of inches of bone because of the above variables. Also not all bone is of the same density. In the pictures you posted notice how the upper part of the skull is made of thin honeycombed bone. A bullet will more easily penetrate this type of bone than for instance, the socket that holds the tusks. The tusk sockets have been known to stop 470 and 500 Nitro soilds. On a side brain shot 3" in front of the ear hole the bullet may only have to pass through a few milimeters of bone along with 8 to 12" of skin, muscle and maybe the must gland. Move that bullet back to the ear hole and the bullet now has to pass through the width of the bone at the back of the skull which could be 6 to 8" of very dense bone. Look at you picture of the intact skull and draw a line from the front ofwhere the tusks come out of the head and carry that line on through the brain. Now do it again from just above where the tusk sockets come out of the skull and again about 6" higher on the skull. You will see a huge difference in the amount of bone that must be penetrated on a frontal shot.

Many of us here, some wih a fair amount of elephant hunting experience are sceptical about trying to come up with a simulated medium to predict a bullets ability to penetrate an elephant skull. Just what type of bone are you simulating? What about the soft tissues that must also be penetrated? Using plywood boards to test penetration can provide some interesting results. But the problem with this approach is that an elephants head is nothomogenous like a ply wood baffle box. The advatage is that the plywood baffle box provides consistent resistence so you get little variation in penetration with the same load thus making it easier to see differences between bullet types, velocity etc. Using live or dead elephants also presents problems because an elephants head is not homogenous meaning that bullets tested on elephants have a large amount of differences in resistance encountered. In my opinion this doesn't discount data taken from elehant carcasses just that you need a much larger sample size that you need in plywood baffle boxes.

465H&H

/

465H&H an Alf!

Thanks a Lot for the fine Pictures and Your verbal Explanation. To fully understand them, I shall familiarize with the Bone nomenclature. Some Physician will help me. This one:



Are those Honeycomb structures in the Elephants bone filed with Air or some Liquid?

asks LutzM

/

Alf,

thanks for the very interesting and thoughtful explanation.

Lutz,

I deduct that for next fall no whitetail deer camp but an elephant cull operation is on the agenda?

/

Alf,

and all Contributors,

this Forum is wonderful: So much Knowledge! So much Help. I really appreciate that. Thank You!











Mammoth

If I look oat the Namutomi Skull, the Explanation, to give a large Area for the Neck muscles to attach to the Skull to be able to lift the Trunk is rather obvious. I assume the Volume Structure contains about 10 % Bone only. In certain Areas near a Joint, on any other Location to bare Forces, the Bone must be denser. The Puzzle remains.

But now being tought, the Elephant skull is a Repetition of Bone and Space, the La Grange Stop boxes appeal much more.

Unfortunately Plywood and Bone are different. While Bone shears at about 120 to 170 N/mm, depending on Direction, length to rectangular to the Fibres (Cross is easier), Wood shears more at 15 N/mm. So that’s an Order of Magnitude earlier.I have no Data of Plywood. Secon Bone is denser than Wood, probably closer to 2 g/ml, opposed to 0,9 g/ml of Wood.

To create an improved Stop box, other Stoppers must be made. We need artificial Bone. I will have to find out, if such Thing exists, or whether it could be made. We have an ancient Clay oven here, making Bricks to restore old Buildings, that I could ask to cast and temper some Plates. Maybe then, it would be easier to compare Bullets and finally sort out the optimal Design for the Elephants Head. That would be my Wish.

LutzM

Lutz,

Data (in English) on the mechanical properties of plywood like that used in my La Grange stop-box can be found at this web address:

http://www.fpl.fs.fed.us/rwu4706/mechproperties.html

Shear strength is from 1.7 - 2.1 MPA (250-300 lb/in2) to 4.1 - 7.6 MPa (600-1,100 lb/in2) depending if shear strength is measured through or in line with plane.

I do not know how to convert this to N/mm.

Remember that emperical results show an almost 2:1 advantage for the Truncated Cone FN over a FMJ-RN or monolithic RN. Refer to Dans article in African Hunter for exact ratios.

Sincerely, Andy

/

Andy and Alf,

Your Data are fantastic, especially those on Bone. I only hat two, now I have the full set. Thius must lead to a simulated Elephant Skull, provided the Penetration Mechanism on Bone is fully understood. Two Models can be applied.

The “Soft Model†means, the Penetrator pushes the Bone aside, just has to shear the Bone. Density Effects ~v² influence Resistance additionally, most at higher Speeds.

The “Hard Modelâ€, like from Tank or Armory means, any Plate will upon Impact be elastically tensioned until it in full Depth brakes. This is tricky. Density Effects ~v² influence Resistance additionally, most at higher Speeds.

For those interested in Pictures, please look at Glasbraker. Glas is a perfect hard Plate.

My Bullet could handle Impact Angles up to 45° almost undisturbed. That means, they continued stable Flight, but at 60° the Bullets tumbled. This would result in a Pentration breake down by a wide Margin. This Tumbling on shallow Angles is probaly the Reason, why comparatively short (to the Bore) Big Bore Bullet perform so well under all Cirumstances. The are not so senstitive to tumbling.

When i see an Elephant with a raised Head some Bone mus be entered under almost grazing Incidence. Tricky Task! Three Possibilities exist to facilitate that sucessfully:

1. A very fast Bullet, "seeing" mostly Mass effects, less the Shear Effects.

or

2. A round Ball or something close (short and fat), not to be too stabiliyt sensitive.

or

3.) A sturdy Bolt stabilised Projectile (remember Lapua Forex)!



Ancient Lapua Forex Bullet (discontinued)

Relative to the Density effects, Bone is not too hard at high Speeds, but quite hard on soft Impact velocities, so something between. A good Model to penetrate Bone therefore must accommodate both Effects in relevant Strength. The “Soft Model†is simple and understood. With the “Hard Model†quit some Thought and Verifying is still needed for Bone.

I will in the near Future work on it and let You know. First some Literature Study is needed. As a Side note, currently I use the “Soft Model†in my Data to predict Bone Penetration. Few have complained, but most shoot smaller Game, where Bone penetration is only of minor Importance, but Meat penetrations count. For this Matter the “Soft Model†Model is preciser than I first guessed, verified many Times on Game and at Norma / Sweden on Ballistic Gelatine as a Control too. Results differed less than 10% from Prediction!

Lutz
p.s.
1 Pascal = 1 N/m²
1 Mpa = 10^6 Pa = 10^6 N/m²
1000 mm = 1 m
1 m² = 10^6 mm²
so 1MPa = 1 N/mm²
first Unit is the SI (scientific) one, the latter one use Mechanics [practical).

/

Alf, Lutz,

You have each found your soul mate!

Hope this comes to repeateble experiments with hunting bullets at hunting vrlocities.

JPK

quote:

Sadly bone does not behave like glass, as glass is typically isotropic and bone shows a specific type of anisotropism called Ortho-tropism.

The very same models of viscous tissue penetration also apply to bone as shown by the studies of Huelke who showed that bone behaves just like muscle during projectile penetration, in that the permanent channel is actually smaller than the largest outside diameter of the projectile meaning that temporary cavitation effect is at work and that bone is in fact elastic, with very strong and definite visco-elastic properties. ( this we know as orthopaedic surgeons who have to marry steel prosthetics to living bone)

Alf,

As far as I know Bone grows along the applied Forces. Therefore the long hollow Bones (Tubes) Properties are definitely anisotropic, take Forces in Length direction maybe 50% more that from the Side. This helps the Hunter on the Ground, shooting the Elephant rectangular in the Leg. That is much more effective than from a Tree from above :=)

I have not read Huelke, but to read Researchers have found, a Viscous tissue model applies to Projectile-through-Bone-penetration encourages e, as that is simple.



Regarding the Elasticity, I remember a Pig I once shot with my 8 3/8†“Dirty Harry†Revolver with a 15,6g .44†Flat nosed bullet on 25 m with about 500 m/s Muzzle velocity. I hit the Pig in about 15 to 30° Angle from the Front, the Pig made a ¾ Circle of 3 m, fell and died. The Bullet exited through the Pelvis and I could see a perfectly round Hole in the Pelvis about Bullet size. I did not Measure it. My Memory just tells me, it had Bullet size.

If a “Hard model†has to be applied, versus “Viscous tissue model “or “Soft Modelâ€, each Bone in the Elephants Head must first be elastic tensioned (eats kinetic Energy), then brake, then milled to Debris and so an and so forth. Nowadays a Computer program can easily be written to do the repetetive Work of say 25 Bone Walls. But all Calculations are in Vein, without knowing how the Elephants Head is quantitatively built.

Monday I will call SYNBONE and hope to gain some Knowledge from there. I keep You posted!

Lutz

Alf and Lutz,

"Visco-elastic properties." Now you are talking! That certainly explains the superiority of FN solids over RN solids and FMJ-RN in elephant skulls.

I am so glad you were able to meet here at AR!

Maybe one of you could explain to me the following emperical observations from my own tests:

1. The 500 grain (458 caliber) Barnes X, an expanding bullet, penetrates 35 inches of water but only 21 inches of plywood. Both expand in similar fashion. Yet water is more dense than plywood.

Is this due to the thickness of the plywood? (3/4 inch or 20mm).

How do you explain?



They both turn over 180 degrees and are recovered base forward.

The bullet that penetrated farther in water actually had more frontal area! Both show much wear on the bearing surface from turning over 180 degrees.

2. A 465 grain A-Square or TCCI brass solid penetrates 50 inches of plywood but only 33-39 inches water. (Almost identical penetration in elephant skull).

This is easier to explain as the blunt RN is very unstable in water despite being a nearly perfect wadcutter with center of gravity near its center of form.

3. Plywood is less dense than paper as Alfs data confirms (thank you by the way). Dry paper, or paper that has not been soaked too long in water, is way too dense to simulate a live animal as many of us have discovered. But the plywood is too dense also. (A 510 grain Remington SP from 458 Winchester only penetrates 15 3/4 inches of plywood but about 54 inches of water).

So the bullets are penetrating more in dense medium (water) and less in less dense plywood, except for RN solid which has a mind of its own!

I mention these mysteries to you both as a reminder that relying on density or shear strength alone may lead us astray.

Hopefully someone can calibrate the synthetic bone to Dans work on elephant.

I would appreciate both of your comments on the above anomolies. Does it have something to do with the hard or soft penetration model?

Thanks, Andy

/

quote:

"When i see an Elephant with a raised Head some Bone mus be entered under almost grazing Incidence. Tricky Task! Three Possibilities exist to facilitate that sucessfully:

1. A very fast Bullet, "seeing" mostly Mass effects, less the Shear Effects.

or

2. A round Ball or something close (short and fat), not to be too stabiliyt sensitive.

or

3.) A sturdy Bolt stabilised Projectile"

Só, all three the above properties combined in one, would result in the perfect DG bullet.

Looks like one of these will be the perfect answer - tested and proved to be just that!

Alf,

You wrote:

"Leonard Euler's formula for penetration would suffice which simply stated that penetration depth would be equal to the projectile energy divided by the square of the projectile diameter times a constant dictated to by the target material. With time a projectile form factor was added to this simple formula. This simple formula is valid for materials of primary cohesive properties and as you correctly pointed out wood supports shear."

That certainly describes both my and La Granges experience with the stop box. Basically, energy divided by unit of frontal area.

5.56mm, 11-13 boards.
7.62mm Nato, 22 boards.
.458 Winchester, 58-59 boards.
.375 H and H, 61 boards.
.450 Dakota, 67-68 boards (465 grain).
.450 Dakota, 70 boards (500 grain).
.416 Hoffman, 71 boards (410 grain).*

Thank you for the concise explanation.

Andy

(*1-10 twist)

//

Alf,

The Barnes X I recovered that is pictured above expanded rapidly which is confirmed by the plywood acting as a "witness plate."

It had very little penetration compared to water which is much more dense.

Weird, and not explained by a failure to expand. It really will be difficult to simulate an elephant skull.

Alf, this is more in the realm of campfire-talk but thought you might be interested:

As an aside, I knew the late Jack Cannon, the inventor of the Glaser Safety Slug, quite well. He was with OSS in Japan after the war ended in 1945, clearing out Communist cells, and had vast experience with a garrote and a .45 Colt.

He devised the safety slug while recuperating from several knife wounds in hospital.

His opinion of the 230 grain FMJ-RN was that the .45 acp was "Suitable for dispatching wounded and executing prisoners!"

He was quite a guy.

Prior to the ready availability of gelatin he recommended his customers tape a slab of bacon fat to an oil can to test his bullets!

I shot cattle killing (feral) dogs with them and we got to be friends.

He considered it an advantage that his bullets would perforate wood or dry wall (barricade material), and still make a base-ball sized wound in human beings.

No doubt modern Police Departments see things differently!

In this case, the penetration through plywood and dry wall is not due to the wall material but the construction of the small blue teflon plug in the bullets meplat.

You are of course correct, that this material does often plug up monometal HP's and many JHP pistol bullets. This is one reason I prefer bonded soft points in the rifle calibers.

The Safety Slug were popular for a time in US prisons and w the air marshalls but they did not have enough penetration for super muscular body builders.

When he was going blind, and in deteriorating health, Mr. Cannon committed suicide by shooting himself in the heart with a .380 PPK loaded with . . . a Glaser Safety slug.

And now, as Paul Harvey says, "You know the rest of the story!"

Andy

Warrior wrote

quote:

It would be nice if Lutz could also explain to us again what forces are at work or the mechanisms at work of a bullet inside an animal.

Hi Warrior,

If animals are hunted, one needs to know, whether the Bullet penetrates into the Life, means, whether it reaches deep enough to kill. Here I develop a simple Resistance model for Bullet flesh penetration. To do so, I assume

1. Within two Calibres length Penetration soft semi jacketed Bullets blast their Tip off, loosing some Weight.

2. If any Bullet flattens towards a Mushroom shape, the Bow crimps within this short Depth.

3. At high Speeds the Bullet looses Fragments. Those Splinters also leave the Bullet within this short Way.

4. For the further Travel on, the Bullet then keeps its Shape.

5. After passing through the Target, Bullets will only leave the Target through the Skin, if the Bullet still moves with certain Speed ( about 30 m/s). Else the elastic Skin captures the Bullet.

6. Flesh shear strength is assumed to be 4 MPa.

7. As long as soft Bullets penetrate only boneless Flesh, they mushroom always into equal Shape.

8. At any Bullet speed the Flesh pull strength remains constant.

The resulting Shear force has to be accounted by the Shear drag = Area * Pull strength.
Bullet retardation = Shear drag + Pressure drag.
Hydrodynamic Pressure drag is such
v := velocity [m/s]
m := mass [kg]
p := stagnation pressure [N/m²]
F := force [N]
a := acceleration [m/s²]
rho := Flesh density [kg/m³]
Cd := drag coefficient []
A := area [m²]
t := time [s]
x := Penetration [m ]

The Brake force is F = p • a.

The stagnation pressure is F = A • ½ • rho • v² in SI-Units

The Stagnation pressure only fully presses right in the stagnation point in the Projectiles nose center. Towards the Side the Pressure levels off. So we use a Drag coefficient Cd to describe the working Force as F = F • Cd

From above experience backed Assumptions, mainly from the same shaped Nose, follows, all impact flattened Bullet resist in Meat with the same Drag coefficient. The fabricated Differences (Spitzer, Round nose Flat nose) flatten always towards the same Bow. Duncan McPherson researched those Drag coefficients and states several Cd's: Cylinder 0.83, Round nose 0.57, Cone 0.52. As he unfortunately states no Value for the typical flattened Bullet bow,

I assume Cd Bow 0.7, which corresponds well with Experience.

Read: Duncan MacPherson´s book "Bullet Penetration": Modeling the Dynamics and the Incapacitation Resulting From Wound Trauma, published by and obtainable from: Ballistic Publications, Dept. NH, Box 772, El Segundo, CA 90245. $39.95 + ship, states further Calculations for Bullet penetration. Look here! Now in second Printing available again!

Integrate Forces along the Penetration

When we know initial Speed V0 Mass and Force at all Way points, we can integrate the Force over the Way to yield the final Penetration. Being too lazy or dumb or modern to integrate analytically, I let the Computer solve numerical Step by Step in JavaScript by the following Algorithm. The analytical solution did Poncelet

Hint: Before you calculate Penetration, cognize exterior ballistic Speed loss. So mix Target V0 Speed at X0 not with Muzzle values. We strictly, only look at the Target.

Force integral over the Way :

The Bullet meets the Target with V0 Speed at X0 Penetration.

The accompanying Stagnation pressure ps = ½ • rho •v² develops (fully in the Nose center).

1st Calculation: Over a very short Way we assume the Speed v = s/t and force constant.
Within this infinitisemal short Distance, we calculate from Mass and Retardation force the resulting Acceleration against the Speed by a = F/m.

2nd Calculation: Above Decelleration yields resulting Bullet speed v1 = v0 – a*t = v0 – F/m*s/v0 at the Step end x1.

Loop 1st and 2nd Calculation until the Bullet stops or the Sow ends.

Lutz
(from ancient Sources)

Lutz,

Its not a typo. Your analysis is too simplistic. The most significant thing that you neglected is, that bullet deformation and target penetration do not terminate at the same time. After the bullet enters the target (animal) its deformation terminates very quickly. However, there is another aspect, that is very important: the material characteristics of the bullet compared against the target. The densities differ by a factor of 10 and the flow stresses by at least that much. Since, according to von Mises rule, the stress is equivalent to the deformation energy per unit volume, a different quantity of energy can be involved in the deformation of the bullet than in the deformation of the target, even though both experience the same instantaneous pressure.

Hope this clarifies the situation,

If I understand your first argument, that the bullet stops "working" in a few centimeters of penetration, while the target continues "working" for the full distance, then yes, that is it exactly.

The first penetration phase is one in which the dynamic pressure acting on bullet and target is greater than the flow stress of either material, so both deform. This is called the hydrodynamic phase, because the bullet behaves like a fluid. They do not deform to the same extent, however; each deforms in accordance with its material properties (density & strength).
When the velocity is reduced to the point, that the dynamic pressure equals the flow stress of the bullet, then the bullet ceases to deform, but continues to penetrate because the flow stress of the target is still much lower than the dynamic pressure. This is called the non-hydrodynamic or rigid body phase, because the bullet acts as a rigid, non-deforming body. Solids behave in this way at all velocities (or they are supposed to). The penetration ceases when the dynamic pressure is equal to the flow stress of the target.

Von Mises rule is a mechanical explanation of elastic and plastic deformation by solids. One of the consequences of the relation is, that it becomes clear, that stress is also expressed as deformation energy per unit of volume. If the flow stress of a material is high, then a greater quantity of energy per unit of volume is required to deform it. Think of it as an energy sponge which can absorb more energy than the target material. So, with deforming bullets (as opposed to solids) a significant amount of the impact energy is spent on the bullet, not the target. At each instant, different amounts of energy are being consumed in the deformation of the bullet and the target. Although these systems are joined by an interface having a peak dynamic pressure, they are treated as independent systems.

I quoted the fraction of 20% to 40% from another source. I have not calculated this. It would not be a simple calculation, but I have been giving it some thought. If I can find a way of doing it without too much effort, I will let you know. There may be a way to extract that information from my hydro code analyses, otherwise it would require to perform a finite element analysis and to integrate the deformation energies at each step. That's more work (I fear) that I had originally intended to put into my penetration model, but there may be a quicker method.

MacPherson seems to be using a modified form of the aerodynamic flight equations to solve the penetration problem. This is crude and not strictly correct but probably reasonably accurate for bullets, that either do not deform or which deform almost instantaneously upon impact (e.g., pistol bullets, which is I believe the primary subject of his research).
Get a reference source on hydrodynamic penetration. I highly recommend any of the papers published by Prof. Manfred Held of Messerschmitt-Bölkow-Blohm (sorry, can't make umlauts). These pertain to the penetration of steel by shaped charge jets, but the mechanics are the same for the hydrodynamic phase of penetration.

You can also adapt the Tate equations. These will be found in any good reference on ballistic penetration.

I was guessing that the flow stress of muscle would be roughly 10 MPa. It may well be 4 MPa as MacPherson suggests.

Have fun!
Hal

(from ancient Communication)
Lutz

Lutz - Was the above from H. Ulfhere?

Yep,
Good Ol' Harold turning all that common sense into calculus for us to admire.

/

Alf, please see PM.