Andy,

I don't know. They don't che their cud.

I have also seen the same effect on pigs plenty of times.

Actually, it is more like you open their gut with a knife and then pulled all the intestines and everything out.

Mike

R.A.,

I assume that you would not presume to use your formula for anything other than non-expanding solid bullets. I make this statement because you have not accounted for bullet expansion or retained weight in your formula.

The C.B.E. - Cartridge-Bullet Effectiveness formula does account for these factors, and is used exclusively for soft point bullets.

Good Hunting !

Pumba,
I do presume to use the BSI on softs and solids. Think of it as a system of rating the payload lifting capability of a rocket. The bullet is the payload that must be lifted into orbit. You, the rocket scientist, must select the proper satellite type to get the job done, e.g., spy satellite or communications satellite.
That is like the hunter selecting the proper bullet.

You, the rocket scientist, must then rate the rocket thrust to see if it can get the job done. That is like the hunter selecting the load based on BSI.

Both aspects go hand in hand. The BSI doesn't claim to tell all the story, just part of it.

I am no rocket scientist, but I have 99th percentile scores on most standardized tests I ever took: ACT, SAT, NMSQE, MEDCAT, IQ

How about describing your formula to me. I am ignorant of it.

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Good huntin' and shootin',
Bwanawannabe, Daktari Ron

Dear R. A. Berry:

I've posted the following essay infebruary, so with the permission of our colleagues, I will post it again, because I'm interested in hear your opinion, Tks!

essay : A Perspective On Bullet Performance
Copyright * 1995-2001 by Gustavo F. Ruiz

When you are heading to the field, with the idea of hunting your favorite game ( of course, a trophy ! ), also another idea might go along, will the cartridge/bullet stand up to the intended target or will it miserably fail to do so ?

Then arises the issue of BULLET PERFORMANCE ( BP ), which expressed in very simple terms refers to the ability of simply putting down game, by disrupting at least one major vital function in one form or another, be by a well-placed mortal shot, shock waves ( wound channel ) or both.

But the real issue is bagging game by one clean shot ( two at the more ), because we all know that by delivering an appropriate amount of inadequate ordnance the goal can be achieved, posing an inhumane dispatch ( remember the poachers ? ). So the baseline for the following argumentation is efficiency in doing what it is supposed to be done by a hunting bullet, again, to cleanly take the game at sight, and of course, overkilling is ruled out (and underkilling, too) , because we are not going after whitetail armed with a .470 Capstick, don't we ?

Much has been said about figuring a mathematical expression that resolves, for once and forever, the question of what is needed or at least which factors play at most when the crucial time arrives ( for both, the hunter and the animal ) and to my knowledge at the present there is no satisfactory expression, be simple or extremely complex, that finishes this problem without further discussion. But we are fortunate enough, to have tons of field, real hands-on experience, in other words, we have information ( valued data ) from which we can extract meaningful statistics, and from here on , we know what works and what doesn't. Let's start by analyzing some known facts, and trying to keep things abstract, for the sake of objectiveness.

As stated before, to cleanly take game, the bullet needs to affect at least one major vital function, but to accomplish this it must reach the vital areas passing through hide, meat and bone, and for this task what is called for is energy, the kinetic type.

We already know, that KINETIC ENERGY ( KE ) is not a good indicator of BP, why, because the real world is a very complex place, where shape, density and volume play an important role, a most one. Consider a high speed bullet fired from a .220 Swift, here we have a very little mass combined with high velocity ( thus favoring KE ) but we don't hunt Cape Buffalo with it, unless we are able to place a shot in the brain, but, even contrary to our desires, it is by no means an adequate bullet. In short, that is a practical demonstration that KE alone is not a good indicator of BP, but we still need it, simply because it is there, we like it or not, and of course without KE the little piece a bullet is will still remain that, a beautiful and useless piece of metal alloy. Nonetheless, both the firearm's industry and NATO recognizes this force as the only scientific parameter positively and widely accepted.

Another physical magnitude often used is Momentum, but to make short a long story, it has the same problems as KE, and by the way, the same virtues.

By this moment you probably have realized that KE or Momentum doesn't take into account to any extent bullet diameter, shape, material or construction design, which is logical, because the formula is considering an ideal physic situation, in terms of hunting reality.

The bullet shape is also, in my opinion, not an important factor when considering Bullet Performance among different cartridges, be spitzer, round nose, solid base or boat tail; because the only appreciated offset is a higher or lower BC ( in a given caliber and weight ) and that means more retained velocity and thus more impact energy ( in a given range ) in short, the ability to overcome air drag is realized at full potential in a given cartridge and within the limits of their available bullets, then a comparison beyond this point is irrelevant, unfair and worst of all, misleading to great confusion.

Experience, from actual hunting situations tells us that very important factors are :

1. RETAINED WEIGHT
2. BULLET DIAMETER
3. VELOCITY
4. BULLET DENSITY DISTRIBUTION
5. BULLET EXPANSION
6. ENERGY TRANSFER TIME
Remarkably enough, the above mentioned factors, are all characteristic of the so-called Super Premium bullets, developed by people with a vast knowledge of hunting ballistics and backed-up by hundreds of performance reports.

Today, many hunters are realizing that they can go a little down on bullet weight by using a well-behaved bullet, whether empirical or not, deep in their souls they know what is putting down more game.

Retained Weight is what is left of the bullet when the travel finishes, exiting or not, and is of paramount importance, because KE is delivered at most of the velocity, being a measure of efficiency, and the most retained, the deeper the penetration ( for a given medium, Muzzle Velocity and Muzzle Energy ) and a high probability of reaching the vitals is obtained, and remember that you need to overcome the opposition of hide, meat and bone.

Bullet Diameter is translated into Impact Energy Surface ( IES ) which determines the initial wound cavity diameter, and this very first instant is what determines if the bullet will or not reach the vitals. Why, because when the IES is large the KE vectors are distributed on a larger surface, and in this way, is easy to understand that shock waves are also playing a different game when acting on a larger surface. In short, the larger the better.

Velocity, is needed for various reasons, first to make useful devices that can throw metal at long distance ( at least we are used to think of our modern high-power rifles as better than a frontloader ) with the less possible drop, second because we need it in large or at least enough quantities in order to reach an appropriate KE that can outdo an animal's tissue.

Bullet Density Distribution, is here referred as to the relationship between caliber, weight and construction materials, which in turn determines bullet length for a given diameter and weight. Note that SD doesn't take this into account, so don't mix or confuse them. Denser materials use less volume for the same mass than lighter materials such as copper. As an example we have a good one in the all-copper Barnes X-Bullet, which is longer in a given weight and caliber than their more conventional counterparts. Is this desirable ?, well, try to forget for a moment about chamber throats and freebore, and view this from an energy distribution perspective. Well, I think that yes, it is a better approach because, while KE is the same, bullet volume and surface are increased considerably. This increment is simply translated into wider wound channels and as the gravity center is displaced forward, the ability to penetrate is boosted. A long time ago, Archimedes taught us that a body displaces its own volume, regardless of mass. The bottom line is, more volume translates into bigger holes. Combining IES and Density we get Impact Energy Volume ( IEV ).

Bullet Expansion is the offspring of design, materials and purpose for which the bullet is intended for, and is desirable only in terms of work at hand, not for itself. We are used to think that expansion is advisable in the light of vast wound cavities, and it is true, recall the previous discussion on IES, and how it is related to bullet diameter where a larger penetration surface means more energy distribution per surface unit. But, there is a payoff in terms of velocity drop ( this is proportional to initial diameter expansion, meaning that more expansion, more velocity loss ), so the bullet will not penetrate deep enough in a given animal. As stated before, sometimes you won't like that the bullet expands, when facing a dangerous animal, maybe wounded first by a bad-placed expansive bullet ( controlled type or not ) what this situation calls is for a non-expanding bullet able to pass through a heavy mass of intermixed tissues and hit a vital organ; remember this is like brain surgery, you must be very precise, because shock waves are minimal and unlikely to help a bad shot. The so-called controlled expansion bullets have the ability to retain more weight per unit of diameter, and this is highly desirable. Hollow points and other designs are means to promote expansion and they work, sometimes beyond control.

Energy Transfer Time, is nothing more than Power, or KE per unit of time. When the bullet hits the animal until the moment it stops, KE drops from some value to zero in a very short time, delivering that energy to the receiving medium ( in simple terms, because some energy is used for other matters ) . What Mechanics tells us is that Power is inversely proportional to time, so the shorter the time employed the more the Power delivered. And here is where KE really plays hard ( meaning bullet weight and velocity ) because a faster bullet needs less time to travel the same distance than a slower one, given the same type and mass. Not only a faster bullet carries more KE it also packs more Power.

And now, I'm going to try to put all the pieces together, not with the intention of giving the hunting world a new idea on how to determine what takes game or at least what is needed for a clean, humane and before all, safe dispatch, but with a rationale from where evolve.

Also I want to warn about the simplicity exposed here, because we are dealing with a very complex phenomenon, which involves many variables, so what I'm presenting here is a practical, simple and simplified way to compute a value related to Bullet Performance, and remember, that there is no such thing as a �magic number�.

For the sake of simplicity I consider the bullets to be cylinders ( a very harmless consideration ), this way external volume is easily determined, after all we are playing with models or approximate mathematical representations of reality, complex or not, and this means that an error is always present. To be exact, this is the main simplification in the way Volume is calculated, then it is the main error source, but the main objective was to remain simple, but it is good enough to resolve performance comparisons.

Remember, the name of the game is ENERGY, in one form or another in the foregoing paragraphs it was always present, but, as I view the question, what we need is an approach that considers and weighs Kinetic Energy in accordance with the other factors that affects a bullet to perform its purpose at best, and at the same time giving consideration to different types, like Solid�s vs. Softpoint�s.

I choose to call it the BULLET PERFORMANCE INDEX ( BPI ), because this designation represents to me the very first and last purpose of firing a bullet while hunting, and is straightforward enough to leave any reasonable doubt about its meaning.

The problem is splited in two main parts, the first is the IMPACT ZONE ( played by IEV ) and the second the BULLET BEHAVIOR ( played by WI and DI ), or the way KE is delivered to the medium it goes through.

Saying this, we have :

� KE = ( W . V2 ) / ( 14,000 . g )

� BS = ( pi . D2) / 4

� IES = KE . BS

� IEV = IES . BL

� WI = WR / W

� DI = DR / D

� BPI = IEV . WI . DI

where, W is bullet weight in grains, V is velocity in feet/sec, g is the universal constant of gravity (32.174 ft/sec2), KE is Kinetic Energy, pi is the well-known geometric constant (3.1415926), D is bullet diameter in inches, BS is Bullet Surface, IES is Impact Energy Surface, BL is bullet length in inches, IEV is Impact Energy Volume, WR is retained weight in grains, WI is Weight Index, DR is recovered diameter in inches, DI is Diameter Index and finally, BPI is the Bullet Performance Index.

Replacing terms, we get a closed form :

BPI = ( V2. p . D . BL . WR . DR ) / ( 56,000 . g )

Here, are considered all the factors I appreciated before as valuables. The IEV ( here is the simplification of volume ) factor takes into account for Weight, Bullet Density ( here goes design and materials ), Velocity, and of course shape ( streamlined ones loss less velocity than blunt ones ). The second and decisive factor ( WI . DI ) weighs expansion and retained weight ( again, design and materials ). Yet most important is using sound principles of Mechanics, oversimplified in order to arrive to a realistic yet easy formula, that, as any right model, must be close to verifiable hunting experience under different conditions, and must realize the knock-down difference of various kinds of bullets.

The length of the bullet is a measurable consequence of density ( mainly, of the materials used and shape to a lesser extent ), and you may have noticed that for example ( both boattail ), a .30 caliber Nosler's Ballistic Tip bullet of 150 grains is taller than a Hornady's Interlock Spire Point of similar diameter and weight. In the first one the hollow cavity and the polycarbonate tip account for the less dense materials and geometry, in the second, a more conventional design, the volume used to obtain the same weight for diameter, combined with shape, is smaller, or about a 10%.

As a rule of thumb I suggest that if you are matching bullets of similar materials and design, give BL a value of 1, or in a case like the previous one you can assign to the Ballistic Tip a BL of 1.1 which represents a 10% increment over the Interlock ( to maintain this scheme of using values greater than 1, the shortest bullet must have BL equal to 1 ) , but be cautious these assumptions are only valid as long as the first one for which a value of BPI is computed is given a BL of 1, and the second one is of similar diameter and weight, otherwise, look for a caliper and take your readings, not your chances.

And now, let me show you some examples, where all the bullets are of similar design and construction, all weigh 150 grains and have the same muzzle velocity of 3000 feet/sec. This meaning similar values of WI and DI ( an ideal situation, maybe right for the same medium ), which allows the cancellation of them, as long as the bullets are of the same before-impact characteristics.

Here, V, represents the bullet's volume, idealized as a cylinder, and corresponds to the factor IEV; also all values are at the impact zone.

Diameter Kinetic Energy Bullet Length Volume ( in3 ) BPI
.308 2997 ft/Lb 1.240� 0.092 275.7
.284 2997 ft/Lb 1.279� 0.080 239.8
.277 2997 ft/Lb 1.318� 0.079 236.8

According to this, the first bullet has a BPI increase over the third one of 16.5%, which corresponds to an equal raise in V, due to the linearity of the example.

Here is presented an example of real cartridges with real bullets, with average values of WR and DR (I know that you can obtain different ones, but they are representative enough), also and for comparison purposes are the corresponding ratings for the L-Factor (L) developed by John Wootters and the John Taylor�s Knock-Out (TKO) values, in this way you can draw your own conclusions and be the final judge.

Cartridge Bullet D W V BL WR DR BPI WLI TKO
.223 Remington Nosler Bal Tip 0.224 55 3100 0.846 39 0.4 50 41 5
.357 Rem Magnum Hornady XTP 0.357 180 1240 0.757 175 0.58 74 44 11
.300 Win Magnum Nosler Bal Tip 0.308 150 3250 1.191 75 0.6 304 245 21
.300 Win Magnum Nosler Partition 0.308 180 2980 1.279 110 0.6 403 296 24
.300 Win Magnum Nosler Bal Tip 0.308 180 2980 1.358 90 0.6 350 296 24
.454 Casull Hornady XTP 0.452 300 1542 0.761 210 0.72 216 150 30
.308 Winchester Nosler Bal Tip 0.308 150 2800 1.191 75 0.6 226 182 18
.308 Winchester Nosler Bal Tip 0.308 180 2550 1.358 90 0.6 256 217 20

Where D is the bullet�s diameter in inches, W is bullet�s weight in grains, V is muzzle velocity in feet/sec, BL is the bullet�s length in inches, WR is the average retained weight in grains and DR is the average expanded diameter in inches. Notice that the BPI, WLI and TKO values are computed at the muzzle.

This ratio shows why the so-called premium bullets are better than the more conventional ones, so the idea is to use the factors properly, weighing one against the other in the search of balance.

Concluding, I'd like to add that the BPI is a shortcut for reality, an expression designed to deal with a complex situation no easily anticipated, but it works if you put some effort on your side to analyze results from a different perspective, and remember that there is no such replacement for experimentation and experience, but this too can be deceived if you don't take enough time to put some light on it.

From here, arises the need of a standard from the manufacturers, giving us compared data on a same basis from where we can make our decisions based on our own hunting situations and intended game, in other words I suggest a baseline, for example recovered bullets fired into the same medium at the same distance ( i.e., ballistic gelatin ), far from perfect at least this would be a common situation in terms of Retained Weight and Expanded Diameter, and it is an improved depart from the one we've today. This a rule in the industrial and scientific world, where without standards communication between developers and users would be chaotic. In the shooting industry, SAAMI is in charge of a crucial role giving standards and tolerances to our firearms and ammunition, so the only extra thing we need is a measurable dimension of expected performance.

A final word, don't surprise me without further discussion, feedback is the basis for progress and those campfire talks are almost invaluable, so don't forget that and keep figuring out things, that from there we evolve, and that was happening since the last million years.

Gustavo,
I admire your multilingual abilities, and the thoughtfulness of your approach to this concept.

The IEV is a new concept for me. I am sure the monometal bullet manufacturer's will recommend it.

I believe you make many valid points, and the IEV concept seems to be a valid one.

The BPI is thus IEV weighted for observed bullet expansion and retained weight.

The BPI which you propose seems to be a good reflection of reality, though you should probably avoid the extreme ends of the available loads.

My only problem with this is arriving at the actual numbers for the bullet expansion and retained weight. Sounds like work to me. Maybe even scientific?

What is wrong with the pseudo-science and numerology of the BSI?

Good huntin' and shootin',
RAB

[This message has been edited by R. A. Berry (edited 07-15-2001).]

I think, the IEV concept is even for this simplified model too oversimplified. In fluid dynamics the length of the moving body doesn�t contribute much to the energy balance. Only the transfer of friction to heat gives a minimal effect, in aqueous tissue only water vapor is acting on the side of the bullet. That means, more volume by lenght translates not to bigger holes.

More important than Energy Transfer Time is the Energy Transfer Location inside the animal. Unfortunately we don�t know the drag functions of bullets in tissue. But most!! of the bullets energy is dissipated on the first few inches of its travel through the animal contributing nothing to the wanted lethal efffects. One reason, why energy or momentum without weighting factors don�t give meaningfull figures.

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Now what the intellectuals are telling us is that the case that holds the most powder and the biggest bullet kills the best..and I agree with that, they have the most whump. and the big dog gets the bone and sleeps on the poarch...

I have no doubt that R.A.'s formula is as good as any...and so was John Taylors. The experience of some of the most experienced hunters in the world pretty well shows these guys to be correct....

------------------
Ray Atkinson

ray@atkinsonhunting.com
atkinsonhunting.com

Thanks Ray,
It is really just for fun and convenience after all. I must say that I think I can back any ballistic Atkinsonism with BSI support. I don't want to beat this dead horse. I know the Bwana Saeed Index is a good tool. If Ray Atkinson and I are the only ones in the world to realize this, so be it.

------------------
Good huntin' and shootin',
RAB

Ray,

Do you think that experience shold be reflected on any mathematical model ?, well I think so, and hope you too, because, that is the very reason for developing such models, to anticipate the outcome and to try to understand a little more our tools.

And here is where reality must agree with the model, not the other way around...

Take, for example the formula devised by John Wootters (HUNTING magazine) where he tried to put his experience reflected in his formula, doing a tremendous mathematical error, that in fact, proved the opposite...so my point is, we can live perfectly well without having to use any kind of formula, mine included, but please if anyone tries an attempt to write one, please remember that we are dealing with numbers, and they have their own rules...believe it or not...

A formula not only has to look "nice" but must behave accordingly, and some people think that they are made up of just mixing salt and water...

Please, our loving sport is full of myths, do ourselves a favor and leave the math to the ones who dare to take the time in order to shed some light...not shadows...

The "intellectuals" before all, were the people who brougth us our tools of the trade, ballisticians among them, with vast knowledge of physics and lots of experimentation, not just "fortune tellers"

Why is some people, so interested in diminish whatever they don't understand ? or worst, trying to make them appear as inexperienced ?

JMHO,

Gustavo,
Relax my friend, we understand what you are saying and we value your excellent contributions. More than a few of us are, presently, just a bit exhausted with the heavy diet of theory, of late. Keep up the good work!