We have a thread here that got some 3356 hits......so someone must be interested (or a chance to show their math skills)!
It's a shame they all did not send Marshall one dollar each in appreciation for their chance to participate!
Now.......since it appears that they all have figured out what causes a quick-kill on game........I would appreciate listening (and learning) about their knowledge.
I would like their input on the following"
(1) Kinetic Energy and how it works?
(2) Momentum Theory?
(3) Hydostactic Shock.....does it really exist?
(4) Energy Deposit.......How and why it works?
(5) Pounds/Foot Theory ......no V squared, just V?
We have tried to discuss this issue two times and have seen it get rather emotional, to say the least!
If I may suggest a drill plan........let each present their findings, based on experience.......then, without chopping each other up, let the others present their theories. Since I do not believe siderules and ballistic programs kill game.....it would be interesting to see what does!
Then the readers can decide for themselves which is valid......James

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Dixie Slugs of Old Town Hammock, Florida
"Home of the Dixie Terminator Slug"

OK, you start.

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You learn something new everyday whether you want to or not.

255gr Barnes .377" bullet
Winchester model 94 in 38-55
1650fps (+/- 50fps) average velocity
75 yards
134lb doe (dressed weight)

Doe only went 15 yards into the woods from the clearing she was standing in when hit.

Bullet entered from the front, just below the spine and was recoverd with 95% of mass, unexpanded, just in front of the anus.

I have no reason to believe that a 158gr 357magnum at 1500fps or such would not have had similar effect from my model 92.

Same goes for a 260gr WFNGC bullet from a 45lc running at 1400-1500fps.

Shot placement is everything.

These 2 items are the same thing. Look at the definition of momentum:

.

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Do not confuse liberal with liberty, especially when the Right to Keep arms is concerned.
Liberals are like Slinkies - Not really good for anything, but they bring a smile to your face when pushed down the staris.

What kills game quick? The loss of blood pressure, make that happen and it doesn't matter what you use

__________________
My sin, oh, the bliss of this glorious thought!
My sin, not in part but the whole,
Is nailed to the cross, and I bear it no more,
Praise the Lord, praise the Lord, O my soul!

Not because of who I am, but because of what HE's done, not because of what I've done, but because of who HE is. -Casting Crowns

OK, since I am not as an experienced hunter as a lot of guys on this forum, I will use my limited (read as dangerous) knowledge of hunting and physics to help explain some things and to throw out a few of my ideas that may or may not pertain to killing animals.
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Personally, I do not know why kinetic energy is used as a parameter when ballistics and effect on animal tissue is discussed. Kinetic energy, as derived in the other thread is not conserved, meaning you won't get out what was put in. As others have mentioned, it dissipates as the bullet deforms and fragments, as tissue is stretched and then returns to its normal state, and as well as other methods.
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With the momentum theory, Mr. Gates the only reference on momentum theory I can come up with is in use with perfect propellors (i.e. no friction). HOWEVER, momentum is different than kinetic energy and momentum is ALWAYS conserved. One of the simplest forms of the momentum equation is (as shown in another post above) P = m * v (where P is momentum, m is the mass of the object, and v is the velocity). With the momentum balance, you can have basically 1 of 2 things happening. A bullet has a collision with an animal and does not exit. The momentum balance would then be m(bullet)*vi(bullet) + m(animal)*vi(animal) = (m(bullet)+m(animial))vf, where vi are the initial velocities of either the bullet and animal; and vf is the final velocity of the two combined.

Using the other way a collision occurs is, the bullet collides with the animal and passes through, exiting the animal. This momentum balance would be
mi(bullet)*vi(bullet) + mi(animal)*vi(animal) = mf(bullet)*vf(bullet) + mf(animal)*vf(animal).
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Here is a little blurp taken from wikipedia.org on Hydrostatic Shock
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The energy deposit or dissipation, was touched on above. If a bullet enters an animal and does not exit, 100% of its kinetic energy is dissipated by deformation, fragmenting, stretching tissue, etc., etc. This does not mean 100% of the energy is used toward damaging the tissue/animal.
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The pounds/foot I am not completely sure I understand what you are saying unless you mean momentum which is briefly discusses above also. Pounds/foot, yields (dimensionally) Force/distance => (mass)*(acceleration)/(distance) =>(mass)(distance)/(time^2) /(distance) => (mass)/(time^2).

However, pounds/foot^2 or pounds/in^2 is pressure and may be useful. I think (this is just what I think so feel free to rip it apart as much as possible) that pressure the bullet imposes on the animal is more of what causes tissue damage. Basically, [force]/[area](bullet) >> modulus of elasticity (animal's tissue).

force = F
frontal area = A
mass = m
acceleration = a

F/A = m*a/A

however, since
1) the bullet deforms and expands, frontal area changes and therefore must be integrated over the range of its expansion
2) 100% weight retention of the bullet itself is rarely attains (if ever) so the mass must be integrated from its original mass to its final mass.
3) as the bullet its the tissue, acceleration is greatly reduced and so it must be integrated over its complete range

so that means a triple integral of dm*da/dA >> modulus of elasticity of the animal's tissue.

I may be thinking too deeply into this and am probably making this a lot harder than what its worth. However, I think that this approach is more analytical (if it can even be solved) and takes into account different size bullets, different shapes, different styles (partition, ballistic tip, bonded tips, etc., etc.). Also, each different type of animal needs to be considered for this type of approach also.

I am not sure if I accounted for penetration adequately but it does need to be considered. It maybe indirectly calculated by using the time the bullet is inside the animal and its velocity. This means another integral for dt.

Like I said I am probably one of the more inexperienced hunters in this bunch, but I do have a strong engineering background (engineering mind you not physics ). However, I think I spent too much time on this today and my boss (academic advisor) would definitely think I spent too much time on it, already, since I need to be tending to turbulence and vegetation. I will still continue to think about this, but I wanted to post what I have been thinking about.


BTW I think shot placement counts more than anything.

__________________
-9r

"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein

sit back, relax and enjoy a homebrew

Heck.... I *always* knew there was a good reason for physics majors.... just couldn't figure out what it was, exactly, till now.

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MikeG

Actually disruption of the central nervous system kills quickest. The loss of blood pressure is a little slower and permits the animal to run 50 or 100 yards or so until lack of blood to the brain causes disruption of central nervous system function.

oh I forgot to mention a third type of collision which affects the momentum balance, and that is a perfect elastic collision. This one really doesn't apply to bullets and animals. This is the collision where kinetic energy is conserved, and most commonly observed (or as close to possible) between billiards balls. This collision type would be pointless if it occurred when hunting because the bullet and animal would go about their normal business, just in different directions, there would be no penetration, no blood loss, no exit channels, basically no dead animal, and a bullet flying around.

__________________
-9r

"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein

sit back, relax and enjoy a homebrew

I have my own equation as to why Kenetic energy is used as a measure of a bullets ability to kill game and the sole factor in so many peoples minds. It is so simple:

S = speed of bullet or its velocity

T = The weight of the projectile

U = Barometric pressure

P = BC of the projectile

I = Ingalls A factor

D = Meplat area of the bullet

So by simply taking the formula with no math skills from top to bottom we see that the final answer is


S+T+U+P+I+D = STUPID

I do stand corrected, a neck shot is about perfect, but really isn't the end result the same, CNS disrupted, heart stops (blood pressure drops), death

__________________
My sin, oh, the bliss of this glorious thought!
My sin, not in part but the whole,
Is nailed to the cross, and I bear it no more,
Praise the Lord, praise the Lord, O my soul!

Not because of who I am, but because of what HE's done, not because of what I've done, but because of who HE is. -Casting Crowns

At risk of stirring this caldren.....we're all pretty outdoorsy people, I think. All we need to do is go out to the woodlot for some real life examples.

6, 8, and 10 lb splitting mauls are pretty common sizes. You can get pretty good swinging speed (equate to bullet velocity) from a 6-pound maul. But I can assure you, you do not get the same wood splitting effect from increased velocity from a 6-lb maul as you do from just picking up the 10 lb maul and whacking a round with moderate velocity.

Now, I'm not going to go into the math, or try to measure maul velocities, etc. I just know that a 10-lb maul is more effective than a 6-lb maul. And I know, a maul head is not deforming like a bullet, etc, etc.

I think we can all agree that the two ends of the extreme, of hyper-velocity in bullets, and slow-mo speed, each have their failings. In real life, there is a happy combination of velocity and mass. Throw in the variables of bullet form and construction, animal characteristics, shot placement, intended effects (explosive dissection in varmint hunting, vs quick death and meat preservation in big game hunting) etc., and all bets are off.

I'm a happy medium kind of person. However, there is a lot of knowledge to be gained by the results of the two extremes.

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SCI Member

niner,
I liked your explaination so that I copied it and saved it!!!!!!!!!!!!

Depends on where in the central nervous system that occurs. If in the head or neck, yeah, that's pretty dead. If in the backbone, it's just incapacitated; the brain is still running the heart/lungs, etc., and it will take a long time to expire if there is no major blood loss. And if you make a "shock" shot - near the central nervous system, horn/antler, etc., that animal is probably going to eventually recover and get up and run off.

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NRA Endowment Member
SCI Member

Interesting and informative! Also for the basic Momentum Theory.....I have seen it applied two ways in ballistics:
(1) Momentum Theory (Monetum Factor)........
bullet weight in hundreds of grains times velocity in hundreds of feet.
Example: 300 gr bullet moving at 2000'/".........
weight of the bullet in hundreds of garins=3
velocity in hundreds of feet=20
3x20=60 mometuum value
(2) Momentum Theory (pounds feet theory)
bullet weight divided by 7000 x velocity in fps = pounds/feet
(refer for both to 1976 writeup by P.O.Ackley?
Now.....all this math is great, but let's add some examples for you all to calculate and discuss:
300 Savage-180 gr bullet at 2500'/" vs Paradox 730 gr bullet at 1200'/"
let's see you run those through and tell me which you feel would have the best lethal pontential on heavy and/or dangerous game........based on KE as well as the rest of the formula), after all this is where we leave theory and get down to gut-piles!.......James

__________________
Dixie Slugs of Old Town Hammock, Florida
"Home of the Dixie Terminator Slug"

where would you like to shoot the animal, the ear or the rear?

I'll check it out, is this a book or an article?

__________________
-9r

"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein

sit back, relax and enjoy a homebrew

Come on! Where would you shoot dangerous game? We are trying to compare two loads against each other!
Handbook For Shooters & Reloaders-Vol 1-Killing Power-Parker O Ackley-1976 issue.
Also in that write up, Packer brought out that the holes in all these formulas, leave out bullet design.....and I agree, as I have said many times before.
Questions that are not addessed in these theoretical formula:
(1) Is it an expanding or non expanding bullet
(2) If is a non-expanding bullet.....what is its Meplat Area
(3) If it is an expanding bullet.......what is the area of its expanded Meplat (nose)?
(4) If it is an expanding jacketed bullet.....did it fragmate (hydroshock?)
These alone can blow the theory calculations! I am still waiting for someone to tell us how KE works on Lethal /Terminal performance. Since it appears so many believe in it, surely they can tell us how it works?........James

__________________
Dixie Slugs of Old Town Hammock, Florida
"Home of the Dixie Terminator Slug"

I was joking

I will try to get my hands on the book, it is the same as the 1962 edition and just reprinted in 1976, that seems to be the only one I can find such as with this one

I think my method would be adequate in modeling how a bullet performs when penetrating tissue. I am sure there are lots more parameters to consider that I haven't touched on, and I can't do the exact calculations without some empirical data. But I feel when you integrate the frontal area of the bullet (meplat to final expansion) you will cover most bullet types. My method is strictly theoretical and complicated, probably more complicated than need be, which is why people might prefer the simple kinetic energy method.

Also, I don't mean to sound pretentious, but maybe unscientific people use the term "kinetic energy" because it makes them sound like they know what they are talking about? Or maybe when new cartridges started coming out, the manufacturers used KE as a selling point, this such and such have 4,000ftlbs where as the other one only has 2,500 ftlbs.

One method of measuring "stopping power" that I am not real familiar with yet, but others might be able to chime in about, is the Taylor Index. This one tries to show that larger bullets can perform better than their speedier smaller counterparts.


just a few of my thoughts

__________________
-9r

"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein

sit back, relax and enjoy a homebrew

At the risk of getting flamed for trying to lay some more humor upon us all....


What would the Taylor KO value be for a 1978 Ford F-250 regular cab traveling at 60 MPH?

I am sure they, along with many more of Detroits finest, have killed much game, both dangerous or not.


MTCW
D

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Darrell


"With a good conscience our only sure reward, with history the final judge of our deeds, let us go forth...asking His blessing and His help but knowing that here on Earth, God's work must surely be our own."

John F. Kennedy

Vitesse Et Puissance

NRA
TSRA

niner......I think you are on the correct path.....keep going and remember Meplat Area (on both expanded jacketed bullets and Meplat Area on hard cast).
I have extended the Taylor concept to the following:
Sectional Density x Meplat Area x Velocity = Comparison Factor. It takes into consideration recovered expanded jacket bullets also. As you know area is not linear with diameter......and is precisely why the larger the Meplat Area on cast works better, all other factors being equal.........and why expanded jacked bullets work better than non-exanding jacketed bullet, all othe factors being the same.
Sectional density is important for penetration (often over done), combined with velocity.
Remember that the Taylor and Thornily concept was based on a non expanding bullet design (mainly a roundnose solid).
This is why I added the Maplat Area into consideration.
Also remember, Parker O Ackley leaned toward ulta high velocity, with the bullet fragmating (mainly with jacketed bullets) inside game. However, he recognised the value of heavy bullets on the opposite end of game weight.
All in all, it comes back to bullet design aimed at a specific game size and distance. After all is said and done, we can only compare bullet's construction aimed at what the shooter is looking for in his game situation........jackected (designed to expand) or hard cast with large meplats.
I am waiting for someone to run up and discuss the two cartridge examples I posted.......Regards, James.

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Dixie Slugs of Old Town Hammock, Florida
"Home of the Dixie Terminator Slug"