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My Response to Criticisms of my KOV theory

 By C. Bekker

 

No theory is above questioning. Only through intelligent questioning, can we make sure exactly what the author had in mind, including certain qualifications that were made, criteria that are subject to change, and any aspect or part that may be judgmental as empirical evidence may not be readily available, especially if there are a myriad of variables that are difficult or almost impossible to ascertain without spending a million bucks on it to find out. Often, theories evolve over time and get adjusted as new facts come to light. For the moment, we have to make do with the best we have available, even though it is not perfect or scientifically proven. The important part for me, is the application of the theory. Does it work in practice? Does it break down in any way? Once this is understood, a theory should be evaluated for its potential contribution, and in our case the understanding of terminal ballistics. I guess some people do not need any theories, they just use their common sense and do what they think is best.

 

Harald Ledbetter, alias HTL, as the ultimate scientist, levelled some criticisms against my KOV theory. I guess nobody is better qualified to do just that. He evaluated my theory from a scientific and an academic point of view, rather than a practical point of view, even though I have not offered it as a science project. Nevertheless, I welcome this opportunity to clarify some aspects as well as referring to his tests in wet paper. I wish to briefly state his criticisms before I respond to them individually:

 

·        Energy is scientifically more correct than momentum

·        Sectional density is not that important

·        The final form of the bullet is not indicative

·        Measurement and records are lacking

·        KOV does not take into consideration the animal to be shot

·        KOV is no better nor any worse than other formulas

 

Energy:

 

As energy is the accepted scientific expression for work, scientists by their very nature will prefer the energy formula. HTL asks rightly .... "Why not kinetic energy multiplied or divided by expanded frontal area, for instance? It may just be a facetious question, but here is the answer.

 

Energy tables, are very poor indicators of killing power. Many people know that through hard experience. In fact, it leads more often than not, to the wrong conclusions and even where energy values are the same for certain cartridges, killing power differs drastically. This means that its broad base use cannot be relied upon. That is why I shy away from the energy formula, just like Elmer Keith, the famous American gun writer of yesteryear. He advocated that momentum was a far better measure based on his considerable experience. Likewise 'Pondoro' Taylor, used momentum instead of energy - and he multiplied it with bullet diameter.

 

When velocity is squared, like in the energy formula, it slants the choice to high velocity cartridges. The energy school of thought, is based on energy dumping and not on how energy is transferred to the target. In fact it ignores entirely the way the bullet performs. Momentum is seen as a driving force that will meet the target ... just like an approaching car, train or aeroplane that collides with an obstacle.

 

My theory explains very clearly, that expanded frontal area cannot be used in perpetuity, as it will impair penetration progressively as the mushroom gets bigger ... its quite simple and logical. For that reason I propose the use of a 'mushroom table', albeit arbitrary but in line with logic and reality. Sectional density is a more useful property of the bullet to use as it correlates with penetration ability. My formula incorporates sectional density and the product of momentum and SD gives the Knock-out value as the following example will illustrate:

 

KOVPRIVATE

Bullet

Muzzle

Muzzle

Muzzle

Sectional

 

Calculation

Mass

Velocity

Energy

Momentum

Density

Bekker's

 

Gr.

Fps

Ft-Lbs

Lbs-Ft/sec

Of Bullet

KOV

25.06 Remington

100

3,150

2,204

45.0

0.216

9.7

45-70 Government

325

1,725

2,148

80.1

0.222

17.8

 

Would you rather prefer to shoot an approaching Brown Bear with the small bore .257 bullet of the 25-06 Remington? The energy tables suggest that we will be better off with the 25-06 Rem! Like hell. My method shows a very different picture. I have no doubt in my mind which cartridge the bear hunter will pick – just go speak to experienced bear hunters.

 

KOVPRIVATE

Bullet

Muzzle

Muzzle

Muzzle

Sectional

 

Calculation

Mass

Velocity

Energy

Momentum

Density

Bekker's

 

Gr.

Fps

Ft-Lbs

Lbs-ft/sec

of Bullet

KOV

300 Win Mag

180

2,960

3,503

76.1

0.271

20.6

9,3 x 62 mm Mauser

286

2,300

3,360

94.0

0.310

29.1

 

Which cartridge do you think the buffalo hunter would opt for? The one with the highest energy level? No, experienced hunters know much better. My KOV method is a far better guide. I can give many more such examples to demonstrate that KOV is far more useful, but let me just state one more. A kudu hunter has to decide which cartridge to pick to shoot kudu at 200 yards:

 

KOVPRIVATE

Bullet

Velocity

Energy

Momentum

Sectional

 

Calculation

Mass

@ 200 yds

@ 200 yds

@ 200 yds

Density

Bekker's

 

Gr.

Fps

Ft-Lbs

Lbs-ft/sec

Of Bullet

KOV

7 mm Rem Magnum

150

2,547

2,161

54.58

0.266

14.5

300 H& H

200

2,180

2,111

62.29

0.301

18.8

 

Will you pick the cartridge with the higher energy value, or the one with higher momentum and sectional density, yielding a higher KOV? I truly believe that the time has come to break away from 'Energy Tables' and start using another yardstick. If a system cannot be relied upon, it ought to be rejected. As I stated before, my formula is a practical guide for the hunter and not pure science. Energy is the most scientific measure of work that we have, and since it is widely quoted on ammo boxes and ballistic tables, I thought that it was highly appropriate to demonstrate, with various examples, that it is in fact utterly useless. Most all gun writers today agree on one aspect, and that is, that 'ENERGY' tables do not tell the whole story. In both cases above, mere momentum will guide the hunter better, even without bringing SD into the equation! Momentum on its own, just like energy also ignores bullet performance, which is a weakness. So it must be used in combination with other factors.

 

Sectional density:

 

HTL discounts the value of sectional density, based on his wet paper tests, that was done on the most unscientific basis imaginable, yielding erratic and confusing results. Differing target medium densities as different wetpacks were used and comparing bullets with differing constructions at different velocities is hardly a test to evaluate sectional density or comparing bullets on an equitable basis. In my opinion, sectional density can only be compared when we have the same type of bullet and the same momentum value as the driving force. I will offer such a load for equitable testing further down. How come other ballisticians such as Mr Halversen and Lutz Möller have proven the value of SD? Does it perhaps lie in the method of testing that is more equitable Mr HTL?

 

My theory states explicitly, that the inherent assumption is that the same bullet type must be used throughout when comparisons are made, as bullet construction of various types of bullets differ drastically, and thus will perform differently. The heavier bullet can better afford to loose some weight than a lighter one, as it ploughs through the animal. Its overall retained weight will thus be higher and so will its terminal momentum. More mass behind a given frontal area does assist penetration. Does this sound logical? That is why bullets penetrate better than round lead balls. Even stubby bullets are not known for deep penetration.

 

Increased penetration is also aided by the lower velocity, at which heavier bullets are shot at, as their set-up rate is slower for one, and fragmentation and weight loss tendencies are less, whereas, lighter bullets that are driven at higher velocities, stand a good chance to over expand or shatter on impact with resultant shallow penetration. So, it stands to reason that a higher SD will generally out penetrate the lower SD bullet. HTL comically asks ... "From where did this insight arise? " Not out of my thumb; that is for sure. In fact various people recognise and advocate the importance of SD.

 

Lutz Möller is using sectional density in his penetration calculator. In his penetration formula, the penetration dynamics are as follows:

 

·        Diameter is the biggest inhibitor of penetration by far

·        then in a direct relationship, the mass of the bullet, and

·        then to an insignificant degree, the loss of velocity

 

The relationship between mass behind the diameter is clearly indicative - that is sectional density my friend. Mr. Halversen did extensive tests to demonstrate the value of higher sectional density bullets and this was published as well. Col. Craig Boddington, an avid hunter, says ... "longer, heavier-for-caliber bullets tend to be more stable, both in flight and in flesh, than shorter, stubbier projectiles of the same caliber.” Are all these people on the wrong track as well?

 

Knowledgeable hunters know that the 7 mm Mauser is known for its excellent bullet performance and killing power, when heavy for caliber bullets (170 gr to 175 gr) are being used. Whereas, when light for caliber bullets are used, it looses its magic and becomes just another ordinary calibre like a 270 Winchester with a 130 or 140 grain bullet The following test, for Mr HTL’s elucidation, will answer the SD question quite satisfactorily:

 

PRIVATE

Bullet

Muzzle

Muzzle

Sectional

Penetration

Penetration

Cartridge

Mass

Velocity

Momentum

Density

With

with

 

Gr.

Fps

Lbs-ft/sec

of Bullet

Solid

Soft

7 mm Rem Mag

140

2,938

587.6

0.248

???

???

7 x 57 mm Mauser

175

2,350

587.5

0.310

???

???

 

The construction of the bullet will influence how its energy will be released (transferred), what weight will be retained and to what extent it will expand. Clearly a controlled expansion bullet behaves differently from a frangible conventional bullet. By the same token, the performance is different for a Solid versus a Soft bullet, even though sectional densities are the same. The construction is different and that is of vital importance. The shape of the bullet's nose can also make a difference in penetration potential as well - this has been demonstrated in various tests with Solid bullets. For example, a 'RWS Solid' out-penetrates a 'Barnes Solid' with its more blunt nose. The Super Penetrator of Norbert Hansen again, out penetrates all other solids - made from brass, with a flat meplat that is smaller than the bore diameter size, with a steel disk at the tip of the nose to prevent any deformation. Also, various tests demonstrated that Solids penetrate 3 to 4 times deeper than Softs. It just depends what Solid, Round nose or Flat Nose, was used in comparison with what type of conventional bullet.

 

SD definitely has some value, but just like energy and momentum, it should not be used on its own to rank the effectiveness of a bullet. Bullet construction must also be considered as playing a vital role and my formula attempts to do just that. It would be silly to compare an expanding monolithic bullet, such as the Barnes-X, with a frangible conventional lead core bullet, even though it has the same SD. SD should be used as one of the elements in a formula to make a contribution. In comparisons to rank cartridges though, we must make the inherent assumption that the same type of bullet is being used throughout.

 

The final form of the bullet is not indicative:

 

HTL has a further criticism ... "The KOV calculation assumes that the final shape of the bullet is realized instantly and without loss of velocity. In actuality, the velocity changes instantly with each micromilimeter of penetration as the bullet gradually expands to its maximum expanded diameter, then assumes its smaller fully deformed diameter that it will hold when the hydrodynamic pressure falls below the effective flow stress of the bullet (at a velocity of roughly 1900 to 2100 fps for most rifle bullets). Though transpiring in a matter of time on the order of a fraction of a millisecond, this is not an instantaneous process and the interval between impact and the termination of hydrodynamic deformation in the bullet dominates the mechanics of the penetration event."

 

Obviously the bullet does not reach its final form instantly and velocity is retarded as it moves along, either to come to a halt inside the animal or to exit at a much-reduced velocity. We all know this. This all happens in a millisecond. To account for this in a formula is near impossible and any such attempt would` complicate the formula immensely, for very little benefit in my opinion. How would this be measured practically or beforehand; do you get my drift? Examining a retrieved bullet can tell you a lot about how it performed and that can be related to the wound caused in the animal. Those with experience of different bullet types, can soon begin to see a trend as to what they do to an animal. Most conventional soft nosed bullets reach its maximum cavity diameter within the first 2 inches after impact – that is before it reaches the vitals, if we assume a shoulder shot. When brittle copper jackets fold back so that the diameter is hardly wider than its original diameter, then it is certainly appropriate to use its final diameter in my opinion. At lower velocities, soft bullets will typically have a bigger expanded diameter, and as such be more effective. Stronger constructed controlled expansion bullets, such as the ‘Trophy Bonded Bear Claw’ and ‘Swift A-Frame’, have slower set-up rates, and typically wider exit wounds are seen. Their wound channels are typically wide and long for a greater distance, and so it also makes sense to use its final bullet diameter. The ideal would be for a bullet to reach maximum expansion when it enters the heart on a broadside shot - seldom will this be achieved with an overly soft bullet. In this argument, we should obviously exclude lung shots behind the shoulder, which offers very little resistance, as frangible bullets at high velocity will explode and disintegrate in the lungs, with amazing effectiveness. Shot placement can be the biggest variable of all.

 

My suggestion was to develop a ‘mushroom table’ that recognises that lethality will differ in terms of the size of the wound channel, and that the expanded diameter of the bullet is the best physical evidence that we have. It assumes a factor of 1 for lethality for non deforming solids, an ideal situation at double caliber expansion as being the best trade of between depth of penetration and size of wound channel with a factor of 2, and a fall off beyond that as penetration will be impaired as over expansion carries on unabated to full fragmentation which is worthless. This table gets applied across the board for all caliber bullets. So, there is no discrimination, all bullets get assessed fairly and on the same basis. This part of my formula is subjective and based on my best judgement. I made this clear up front. If there were a better way to deal with the question on the size of the wound channel, I would have made use of it. I consider my approach far better than the one that says the ‘caliber of the bullet to the power of three’ equates to the wound channel. Is my intuitive judgement wrong, just because I cannot proof it scientifically to HTL's satisfaction? If I must wait to have everything proven scientifically, then my theory would never have been published ... is that preferable?

 

We need to recognise that the hunting field is not a laboratory and therefore does not lend itself towards finite measurement. The mushroom factor, as I have stated categorically, is not a precise or absolute factor, but when applied for all calibers across the board, we have at least a common denominator for relative measurement. Impact velocity will affect expansion. HTL also stated ... "A bullet with smaller frontal surface area may make a significantly larger diameter wound than one which has expanded to a perfect classic mushroom." I reject this statement as a general truth and know of no such bullet on the market. When challenged, HTL replied "You know perfectly well that no specific bullet is being described and that I am not arguing in favour of bullets with small frontal areas.” All my KOV system really says, is that the bullet with the bigger expansion will create a bigger hole as I have witnessed on shot animals. I do not base my opinions on wet paper. Even if we use solid bullets at the same velocity, a 458 Lott will create a bigger hole than a 9,3 x 62 mm.

 

Measurement and records are lacking:

 

HTL states further … “When the support of real world field experience is drawn upon for evidence, it is entirely subjective, simply the conventional wisdom.”

 

I say again, the hunting field is not a laboratory. Hunters generally never measure and document wound tracks as they are not scientifically minded ... they are hunters. Nevertheless, they are the ones with the most practical experience and this cannot be ignored. I further submit that practical experience will guide us for the next 100 years, just like it guided us for the past 100 years. No amount of scientific measurement, as envisaged by HTL, will change that. The wealth of experience among notable hunters, past and present, cannot just be ignored and their judgement cannot be that wrong, unless we are relegated to a subordinate specie, with very little interpreting skill.

 

My theory correlates with my observations in the field and even if it is only 90% correct in terms of lethality, it is still valuable. My observations were made over a period of 35 years, long before I considered writing an article or formulating a theory. If an outcome is substantiated by results obtained in the hunting fields, it can thus claim to be valid and factual (scientifically correct). I offer a practical guide that works; there is no doubt about that. "Pondoro' Taylor's theory is perhaps the most instructive guide for elephant hunters, and he too, would not have received an honorary doctors degree in science, but who can tell him anything about elephant hunting? The fact is, it worked for him and many others.

 

KOV does not take into consideration the animal to be shot:

 

HTL then proceeds … “KOV does not take into consideration the animal to be shot.” This is presumably another drawback.

 

I am really dumbfounded by this comment. The animal or type of animal has nothing to do with assessing or ranking of calibers; KOV is only a gauge, it measures lethality. What one does with that lethality, is another matter - shooting a dassie or an elephant. Matching a particular caliber and bullet combination, is judgemental and the choice of the hunter and can vary from animal to animal. For example, I will opt for a controlled expansion bullet for buffalo and a non expanding solid for elephant in my 9,3 x 62 mm. The same calibre, but two different applications. Clearly, the role of bullet construction and behaviour makes the difference!

 

We know very well that animals can be killed by smaller and marginal calibers with good shot placement. Shot placement is the skill of the hunter and plays a decisive role in killing, but it is a separate issue. Also, it is the hunter’s choice to decide what power he needs to apply in the killing process. Experience counts more here than science. KOV only ranks calibers on a relative basis, but when bullet performance come into play, i.e. weight retention and expansion that affects depth of penetration, we are then better able to assess lethality. Only through experience, do we know how a certain type of bullet performs. On average we know expansion and weight loss tendencies of a specific bullet. It is a dynamic situation and this knowledge must be used in the KOV formula – that is what my theory calls for explicitly to more closely model reality!

 

Once we understand all the key variables that play a role in terminal behaviour, my KOV system will guide you, but it is not absolute. Unlike other formulas, such as ‘Optimum Game Weight’ or ‘Vital Game Weight’ I do not specify a certain weight or size as I do not believe in that. For example, OGW specifies an animal weight of 371 pounds at 150 yards for a 7 x 57 mm with a 175 gr bullet at 2,440 fps. Hardly adequate for kudu - this is absolute nonsense! This caliber has proven itself in the field to be absolute ideal, even more so today, with the availability of premium grade bullets. We do know that the more powerful 30-06 Spr have failed many times in the past with frangible soft point bullets. We can thus say that this calibre/bullet combination is less lethal for short-range work. High velocity at short range causes the bullet to loose more weight and it either over-expands or shatters the bullet. My KOV system recognises this dynamic situation. Any ‘killing’ formula, that ignores bullet performance entirely, is not worth the paper it is written on. Bullet behaviour is different for each bullet type at various velocity levels – bullets are not created equal and have different threshold strengths. The subject is indeed complex.

 

KOV is no better nor any worse than other formulas:

 

HTL concludes by saying ... "In the final analysis, the KOV is no better nor any worse than the TKO, OGW or any of a score of other formulas trying to get at the answer. They all fail.KOV looks like it has a little more thought behind it than many such calculations.” HTL says my KOV formula satisfies my preconceived notions about how things work and it is based on popular ignorance of terminal ballistics.

 

I beg to differ. None of the other formulas incorporate bullet performance. My formula is not based on unsound logic, or factors that skews the comparison. My formula includes all the main factors that do play a vital role in terminal behaviour. Every element that is used, gets its full credit. Whilst I attempted to model reality, I do admit that it is not perfect and never will be. I do not have a preconceived notion as to calibers or how things work. KOV is simply a way of modelling a scenario. My formula leads me to an answer and I believe in it, because it makes sense to me and it works for me. I do not work back from the answer to the question as is hinted above.

 

Another reason why my formula gives a good prediction of lethality, is because it recognises the role that the construction of the bullet plays ... how it transfers its energy ... by way of diameter expansion and weight retention. Even this may not be perfect, but it is as close as I could get without over complicating the formula. My formula is the only one out there that incorporates these two elements.

 

Also, the striking velocity at range ... i.e. it recognises the ballistic coefficient as well, as game is seldom shot at muzzle velocities at point blank range - this makes my formula more real and practical. The value of my formula lies in its comparative ability, rather than in its absolute correctness as expressed in a single figure. Absolute figures for killing is impossible and that was never my objective. It would become way too complex in any event to satisfy a scientist. My formula is built on the foundation of Taylor, but I took it a few steps further:

 

·        I use the bullet's SD instead of its diameter as it has a bearing on penetration

·        I account for striking velocity at various ranges as it impacts on terminal momentum

·        I account for bullet weight loss as it impacts on terminal momentum

·        I use a mushroom factor to balance the size of the wound with impaired penetration

·        Extended the use to soft nose bullets for a wider application of killing game

 

Taylor made it clear … “It must be clearly understood, however, that they make no pretence of indicating “killing power”. On the contrary, they are only to be considered as a basis for the actual knockdown blow delivered by bluff-nosed, solid, metal covered bullets when used for head shots on heavy, massive boned animals such as elephant.”

 

HTL says that both Taylor’s system and my system do not work. Fairly presumptuous I would say as both systems proved themselves in the field. How does HTL define failure – perhaps because it does not meet his scientific standards? HTL can construct the toughest scenario for me, and I will solve his dilemma. It is my humble opinion that my KOV formula provides the hunter with the best possible advise out there. Many Professional Hunters have come back to me with praise for the underlying logic. I do not claim my theory to be a scientific dissertation - it can never be - killing is far too complex for that as results are almost always marred by different shot placements, especially when bone is encountered at an angle' like it invariably happens. The objective is not to discuss shot placement, as that is the skill of the hunter that stands separate from ranking ‘caliber/bullet/load’ combinations in terms of lethality.

 

So, here is my formula, expressed in a basic and simple format, comparing two different loads that are performing differently. Note the impact of the striking velocity on weight retention and expansion of diameter. When we start out with a lighter bullet, the induced momentum (forced applied) will be less and so will the SD of the bullet (property of the bullet). Ordinary people, without a degree in quantum physics, can use my KOV system with relative ease.

 

Bekker's KOV  =  Terminal Momentum x SD x Mushroom Factor

 

                     =  (Retained Weight x Striking Velocity) x SD x Mushroom Factor

7 x 57 mm   =  (130 gr./7,000 x 81% retention x 2,750 fps) x .230 x 1.125 times

                     =  10.7

7 x 57 mm   =  (170 gr./7000 x 93% retention x 2,100 fps) x .301 x 1.35 times

                     = 19.3

 

Building a model on HTL's confusing wet paper results would not be feasible in my opinion, but perhaps HTL can develop a system for us, based on his 'scientific work', to guide us ignorant mortals, without making us shoot wet paper every time. I presume it will incorporate all the scientific variables, in the finest detail, so we hunters can get a better fix. I am just wondering how ‘paper’ wounds would be related to flesh wounds in animals – probably with another correction factor (another pitfall). Beware, if science is not substantiated (verified) by reality, it can no longer have any claim to the authenticity of its results, no matter how careful, or repeatable and accurate, measurements were taken. Final proof is always in reality, on game, and not in wet paper. Hopefully some scientists will agree with me.

 

 

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