This is a double entendre to get your attention.
Regarding the BS Inhibitor/Bwana Saeed Index:

I have finally gotten a copy of Duncan MacPherson's book (Bullet Penetration) for my own perusal. I am very happy with what I see, except that I don't believe he dealt with twist rates and bullet RPM's at all.

His book intensifies my support of the BSI concept. Note however, that his work is mostly aimed at the handgun with bullets around 1100 fps, largely for law enforcement applications. His main purpose is to present a model of the dynamics of bullet penetration in tissue simulants. He says: "Unfortunately, there is no single term that is universally accepted and used for the wound incapacitation of interest; many terms have been coined and used ... The new term used herein is WTI, for Wound Trauma Incapacitation; this term refers to the production of an incapacitating wound by the bullet parameters (velocity, weight, shape, diameter)..."

There is a parallel here with the BSI nomenclature, which has been arrived at with helpful suggestions from forum members. "BSI" is an expression for exterior ballistics of big bore rifles suitable for hunting (and stopping with higher BSI values) the Big Five of Africa.
"WTI" is an expression for terminal ballistics of handguns primarily.
The Atkinsonism for BSI is "whomp."

WTI is based on: velocity, weight, shape, and diameter of the bullet.

BSI is based on: velocity, weight, sectional density, and diameter (caliber) of the bullet.

Andy once tried to tell me that the BSI had momentum squared as its basis, but of course this was wrong. I was not "upset" with him, but just wanted to quash a falsehood. Note that if you have a term for velocity and a term for bullet mass (or weight) multiplied together, as in the BSI, then this is momentum. Factoring in terms for sectional density and caliber do not duplicate momentum or sguare it.

Sectional density is derived from caliber and bullet weight, but it is defined as a unitless convention, as I pointed out to Norbert, hence has no effect on the order of the momentum (and there is no second velocity term anyway). Therefore, momentum is not squared.

Including the sectional density weights the formula for penetration ability. Factoring in the straight caliber term weights the formula to give credit for bullet cross-sectional area in wounding or "whomp" delivery. The Atkinsonism for this is: "Bigger bullets make bigger holes."

Now for the "Kinetic Energy vs. Momentum" critique.

Duncan MacPherson:
"Most people have a concept of energy and its meaning in their own mind, but this concept is usually simplistic and incomplete at best for those individuals without technical training. ... On the other hand, every now and then someone wants to analyze or think about a problem involving energy, and when they attempt to do this without really understanding energy or other thermodynamic concepts the result is unfortunate. ...
"Any attempt to derive the effect of bullet impact in tissue using energy relationships is ill advised and wrong because the problem cannot be analyzed that way and only someone without the requisite technical background would try. ... Newton's laws describe forces and momentum transfer, not energy relationships. The dynamic variable that is conserved in collisions is momentum; kinetic energy is not only not conserved in real collisions, but is transformed into thermal energy in a way that usually cannot be practically modeled. The energy in collisions can be traced, but usually only by solving the dynamics by other means and then determining the energy flow."

Note: with the BSI we are talking about collisions-to-be, not the terminal ballistics, but the exterior ballistics. Even when you get down to the terminal ballistics, you have to use momentum to trace the kinetic energy dissipation, which is all turned into heat. Duncan MacPherson continues:

"All of this energy is quickly (much less than a second) transformed into thermal energy. The energy magnitude is far too small to create any thermal trauma to tissue (2300 foot pounds of energy will raise the temperature of 3 pounds of water about 1 degree Fahrenheit.)."

Duncan MacPherson's summary at the end of chapter two:

"Attempts to determine bullet effectiveness or assign WTI by assessing bullet kinetic energy are doomed to failure for two interconnected reasons:

1) damage is done by stress (force), not energy.
2) an indeterminate, but usually large, amount of the bullet kinetic energy leads to tissue stresses that are not large enough to cause trauma (especially in handgun loads)."

Well, it seems that I, the blind hog, have stumbled into quite an acorn, this Bwana Saeed Index. It is good for what it was meant to do: BS Inhibitor. BSI values will not lead you astray in comparing the effectiveness of the big bore loads.

To avoid the shaky fringes of ridiculous concocted projectiles, like the needles and frisbees and hand thrown bowling balls, limit the BSI application to sporting rifles of .375 to .700 caliber, and velocities centering around 2450 fps, for example 2000 fps to 2900 fps. You won't go far astray.

[This message has been edited by R. A. Berry (edited 06-04-2001).]

I forgot to mention the few words about sectional density I have found thus far in the MacPherson book. With handgun wound incapacitation the goal is not to get too much penetration. With the big bore rifles, however, penetration is very important. Hence, any ranking formula would require a sectional density term. The title of his book "Bullet Penetration" is ironic in the sense that the LE officer's goal is to avoid excessive penetration. From page 142:

"Effect of Sectional Density"
"An increase in initial (undeformed) bullet sectional density will cause equivalent expansion at lower velocity. Greater expansion occurs at the same velocity because the decelerating forces must act for a larger time interval to reduce the bullet velocity (the decelerating force and the stagnation pressure causing deformation are highly correlated). This effect can also be quantified analytically in principle, but is complex because equal bullet distortion requires an equal force integral over position (of the distorted bullet surface), whereas a changed sectional density changes the force integral over time. The relationship between distorted bullet surface position and time is difficult to model. A very crude analysis shows that a 20% increase in sectional density would lower the velocity for equivalent expansion by about 5%."

On page 281, in discussing recoil of handguns, MacPherson says:

"This simply means that cartridges that produce greater wound trauma have greater recoil. This is illuminating, but not surprising. Here, as always, there is no free lunch; the laws of physics are inexorable, and there is no "magic bullet" that gives something for nothing.
"The second tradeoff of interest ... is the fact that higher velocities produce lower wound trauma efficiencies for any bullet weight. This result is also not a surprise; experienced hunters know that it is easier to get penetration with a heavier, slower bullet than a light, fast bullet. This tradeoff between bullet weight and velocity is illustrated for several dynamic options in Figure 11-4 relative to reference conditions of a 180 grain bullet at 900 ft/sec. The curve of constant bullet momentum (mV) also has constant recoil energy. The curve of constant kinetic energy (1/2mV*2) has less recoil with lighter bullets; this is the attraction for the energy advocates who seek a "something for nothing" magic bullet."

The Atkinsonism for all this is: Bigger, heavier bullets make bigger holes and kill better.

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Good huntin' and shootin',
RAB

[This message has been edited by R. A. Berry (edited 06-05-2001).]

Ron,

I still think your BSI requires the figure to be discounted if the velocity is under or over a certain figure.

Maybe 2600 f/s.

Unfortunately not have shot large game I don't know if it applies there.

But it certainly does with smaller calibers on smaller game.

However, I am starting to think that the Barnes X type bullet my be a higher velocity.

I always thought that Taylors formula had merit by giving credit for diameter increase but not the square of it, since that would reduce the velocity of penetration and perhaps offset the gain made by a bigger diameter.

Mike

Mike375,
I agree with you on the velocity issue and the caliber versus cross-sectional area point you make.

For simplicity, I am centering the velocity around 2450 fps and going no higher than 2900 fps and no lower than 2000 fps, +/- 450 fps, for presumed validity. This pretty well covers the commonly used big bores, with the proviso that it may not be as accurate at the extremes of high and low velocity.

Anyway, there is no other method that I know of that can rank the big bore exterior ballistics and "Whomp" as well as the BSI. It is a gun nut thing that seems to reflect real world experiences fairly well. It is the improved Taylor KO value.

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Good huntin' and shootin',
RAB

Da, big bullets at high velocity kill stuff. I guess John Taylor, my saint, was right. Even though I got one, I guess St. Taylor didn't need a Ph.D. to figure that out.

Will,
Even though John Taylor was the Grandaddy of Big Bore Philosophy, he was no saint. Butt(sic), even some of the great philosophers of Greece had their peculiarities like Taylor. You must surely admit that factoring in the sectional density term is an improvement on the framework that Taylor laid out for us gun nuts.

I prefer to reserve that exalted title for Saint Finn Aagaard.

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Good huntin' and shootin',
RAB

RA,
St. Aagard always said that the 458 just made bloody bigger holes, therefore it was better than his beloved 375 for ugly stuff...He firmly believed that "whomp" came from cross section and the only way to increase "whomp" after 2250 FPS give or take 50 FPS was to increase the cross section..Many of Africas old elephant hunter by this theory...I see little difference in my 450-400-3" at 2150 FPS and my 404 loaded to 2653 FPS as to knockdown, but I can see the difference in a 458 Lott and the latter. The Lott wins hands down..

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Ray Atkinson

ray@atkinsonhunting.com
atkinsonhunting.com

Mr. Berry:

I always figured that anybody that favored a 458 Win couldn't be all good! I thought Mr. Aagaard's book was rather uninteresting. I corresponded with Mr. Aagaard when he was in Texas, and found him to be a very personable and helpful guy. So nothing, absolutely nothing, against Mr. Aagaard. He seemed to be a nice guy.

But, I still vote for St. Taylor.

Ray,
This little mathematical accounting method for big bore ballistics called the BSI is really in complete agreement with your observations. It gives little credit for added velocity. The only way to make significant improvements in the BSI for a given caliber is to increase the bullet weight and hence sectional density. This more than compensates for the small changes in BSI with the slightly reduced velocities with the heavier bullets.

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Good huntin' and shootin',
RAB

Will,
Forgive me for casting aspersion upon the character of John Taylor. He was only human back then, but now ... he is a Saint, if you say so.
I believe St. Aagaard relied upon handloads that pushed a 500 grain .458 bullet at 2150 fps, and he never had any of those bullets bounce off a cape buffalo.

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Good huntin' and shootin',
RAB

RAB,
in different topics we arrived at the conclusion, that neither kinetic energy nor momentum is suitable for a ranking of the effectiveness of hunting bullets in terminal ballistics. It has at least to be weighted by factors like sectional density, mass, frontal area, shape etc.
McPherson is using a similar approach and weighting momentum with shape and frontal area or diameter.
But there is no need to divide the amateur ballisticians world into two sides, the energy based group and the momentum supporters. His saying, that someone attempting energy discusssion is not really understanding thermodynamic concepts is rather arrogant. "Newton�s laws describe forces and momentum transfer, not energy relationships.".....but also not terminal ballistics

Kinetic energy and momentum of the moving bullet are strongly correlated. All starts with the rifle acting as a thermodynamic heat engine, applying KE to the bullet. Calculating the momentum is a kind of weighting with the mass and useful for describing momentum transfer in elastic collisions.
But the impact on and the travel through the target is very inelastic and complex. The momentum is not conserved! (as McPherson states). When the energy is dissipated and converted into heat, also the momentum disappears. At any point of the bullets path the momentum is KE divided by velocity. When velocity approaches zero the momentum also becomes zero.
To produce wounds in the animal, the bullet uses its KE to deliver the forces needed for destroying the tissue by cutting, crushing, stressing etc. The KE is theoretical conserved, but at the end converted into heat energy, which at this level is not effective in doing additional trauma. The heat is the only energy left, the cutted and crushed tissue has not got additional forms of energy.

Some statements of McPherson are wrong:

1)damage is done by force, not energy....is a misleading sentence. The force is and can only be supplied by the kinetic energy. You may ask, how the forces are working and may not set energy equal to killing power, but to neglect fully the term energy is a bad mistake.

2)a large amount of the KE leads to tissue stresses that are not large enough to cause trauma....Here McPherson refers to the temporary wound cavity which, dependent on the kind of tissue, can recover with lower energy bullets, but with big bores it can cause lethal effects.

Other statements are very confuse or only applicable to handguns: "higher velocities produce lower wound trauma for any bullet weight" or "it is easier to get penetration with a heavier, slower bullet than a light, faster bullet". That is basically not true and can be observed only by chance and is then caused by secondary effects like bullet construction, interaction with the terminal, characteristic of the mushrooming with time etc. Following McPh we should go down to 900 f/s?

BTW: It is well done to limit the BSI to the big bores at velocities around 2400 f/s. But if someone is discussing momentum as the physical property of a moving body you can apply it to bullets and bowling balls as well for comparision.
If SD up to now is a unitless convention, what about to use a SD of the magic 0.33 as 1 Saeed? SD broken down to its dimension is mass per area.
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[This message has been edited by Norbert (edited 06-08-2001).]

Give them hell, Norbert. I think it looses something in the translation to English, but physics is physics no matter who tries to redefine it.

I'm with you (as near as I can tell!).

Will

Norbert,
I agree that there is more than one way to skin a cat. You make good sense. Actually, I do not presume to be involved in terminal ballistics with the BSI. Field and game characteristics and all the different bullet types would make this too cumbersome to be practical. One could never apply a theoretical model to the fight or flight response of various critters in different states of vigor, etc., with any reliability.

The BSI is devoted to exterior ballistics, to quantify for comparison purposes the payload delivery capability of the big bore cartridges. The hunter must be wise or experienced in bullet selection (type of bullet construction), and skilled in bullet placement, for practical application. This is the art of the hunter/rifleman, tempered by a little simple arithmetic, the BSI.

What you are saying about momentum versus kinetic energy is what I have been trying to point out for some time. They are both based on a given mass at a given velocity. It seems to me that the big bores are more amenable to ranking on a momentum basis. The smaller caliber, higher velocity bullets designed for explosive effect or hydrostatic shock effect would seem to be more appropriate for a kinetic energy based system. Apples and oranges.

With the big bore we want to break bones and penetrate with a long and wide permanent cavitation or wound channel. The smaller bores work a little bit differently. Less mass and more velocity is their modus operandi, and that seems to scream for a kinetic energy method. Momentum is less meaningful for small bores, and kinetic energy seems less meaningful for the big bore. The big bore depends equally on mass and velocity. Practical observations show diminishing returns for big bores with higher velocity past some point, and failure of the bullet to punch through is more likely at the higher velocities. This seems to spell "momentum" for big bore ranking, so as not to over-credit velocity, which actually produces diminishing returns past a certain point. Again, not so with most small bore applications, as in varminting and long range big game effectiveness.

Of course energy is conserved, but kinetic energy is quickly transformed into the potential energy of stretched elastic tissue in the cavitation process, which then rebounds almost instantaneously into kinetic energy of rebounding tissues, noise, heat, and misdirected activity that is hard to trace and quantify, like rupturing bullet integrity. That thermal energy is really kinetic energy on a molecular basis, as heat makes the molecules bounce around in Brownian motion at higher molecular velocities. As stated above, a lot of kinetic energy can be soaked up by practically negligible temperature change in the target. Like shooting a bullet into a tank of water that is sufficiently deep to slow the bullet to a halt in the water before striking the tank wall or bottom, all the bullet does in expending its energy is to raise the tempersture of the water, and displace the water (raises the water level a smidgeon) which is a conversion to potential energy storage by a tiny amount, off course.

Momentum is more easily traced in its dissipation.

As for the unit "Saeed" representing a sectional density of .330, I think it should remain a dimensionless ratio, as it is really only the ratio of the weights of two bullets of the same caliber. Besides, I don't want to be seen as kissing up to Saeed too much! I can only do so much brown nosing without losing my credibility.

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Good huntin' and shootin',
RAB

[This message has been edited by R. A. Berry (edited 06-07-2001).]

Gentlemen:
No matter which way you approach this problem. I doubt if you will ever come up with a true source to define your objective.
This has been tried for over onehundred years. I sumit that experience has proved to be the best related source for this problem. The British probaly figured it out some time ago, or else, stumbled onver it by accident many years ago. In other words a 500 grain bullet at about 2300 fps will do for anything we have left living on this planet. (But it is fun to talk about)
George

I believe George nailed it down and RA Berrys theory is sound as any...

I KNOW a 577 will slap a Buff down better than a 416, 458 Lott or anything I've seen, but that slap goes both directions and I'm just fine with a 416 Rem.

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Ray Atkinson

ray@atkinsonhunting.com
atkinsonhunting.com

Ray and George,
Your wisdom shines forth. That just about sums it up.

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Good huntin' and shootin',
RAB