Put a bunch of hunters together at a favorite watering hole, or around a hunting campfire, and at some point, talk will almost certainly turn to stopping power, killing power, and matters relating to the way a bullet performs on an animal that is on the receiving end. You are bound to hear about kinetic energy, Taylor’s knockout formula, momentum theory, and other impressive-sounding terminology that compares the terminal ballistics of one bullet to another.
I too have spent many hours debating and arguing with fellow amateur ballisticians about the efficacy, or lack thereof, of bullets and their effects on target animals (or people).
I think it comes with age but, with close to sixty summers behind me, I have come to realize that we are extremely gullible creatures, and will readily believe almost anything that appears in print–especially articles written in gun magazines. We accept in most cases what is written as ‘gospel’. I am no longer as gullible as I used to be in my younger days–I now question and put everything to the test.
When it comes to terminal ballistics, the effect that a bullet has on a living target, I began to question the prevalent thinking many years ago. Based not on any personal profound knowledge of ballistics, which is a very complex science, but on personal experience, when on many occasions, I was astounded to see how many foot-pounds of energy an elephant or buffalo could soak up before finally dying.
My suspicions were recently confirmed by the work of a professional ballistician, who chooses to remain anonymous, in a series of excellent articles that exposes most of what we have come to accept as sound ballistic principles, as overly simplistic at best, and pure myth at worst.
His arguments are absolutely sound. So let’s have a look at some of the ballistic myths he puts to rest.
The popular misconceptions he addressed were:
- Taylor Knock Out (TKO) formula
- Momentum and “stopping power”
- Threshold of wounding potential based on kinetic energy
- Optimal Game Weight (OGW) formula
- “Energy dump”, “over penetration” and “hydrostatic shock”
- Lethal Index formula
- Knock-Out Value (KOV) formula
According to Taylor’s formula a hand thrown baseball will have twice the TKO of the standard nitro express load. Bouncing the baseball off the noggin of an elephant is unlikely to produce any positive results
Taylor Knockout (TKO) formula
Taylor’s Knock Out (TKO), a formula based on the experience of the renowned African hunter John Pondoro Taylor, is one close to the heart of many amateur and (supposedly) professional ballisticians and hunters alike. It states the following:
TKO = Bullet weight (pounds) x Impact velocity (fps) x Bullet diameter (inches).
Now in mitigation of the formula, it must be remembered that Taylor suggested it at a time when there was a cult following of small caliber, high-velocity hunters who ventured into the African bush and often experienced dismal failures, unfortunately with fatal consequences. His formula was no doubt in reaction to this and included his bias towards the bullets and cartridges he favoured and knew to work reliably.
- The problem with this formula is the following:
“This formula is as misleading as any kinetic energy figures…I have seen”. The inadequacy of this formula is soon exposed, when it is pointed out that a hand-thrown baseball has no less than twice the TKO of the standard Nitro Express (NE) load! - Taylor himself admitted that there was no appreciable difference in the killing performance of the various .400s, .415s, .450s, .465s, .470s, .475s, and 500s on dangerous game when loaded with reliable bullets of sound construction (Ah ha! Here lies the rub.). The TKO, as most commonly interpreted, exaggerates any difference that might exist because it makes the bore diameter equally as important as the velocity. When comparing a .450/.400 NE and a .500 NE using his formula, the latter is calculated to be 55% more potent, even though Taylor himself admitted to them being very similar in killing performance. So, things do not appear as they seem.
- It must be stated in Taylor’s defense however, that he never intended it to be used as an indicator of killing or even “shocking” performance for hits on the body. He indicates that the “stunning” effect calculated by his formula applies for the most part to near misses of the brain on an elephant. He made the point that even a “stopping rifle” was ineffective with poor shooting: “Both barrels from a .600 in the belly (of an elephant) will have little more apparent effect than a single shot from a .275 in the same place.” (African Rifles and Cartridges, Taylor. Page 59).
- Promotion of this formula is a prime example of the careless way in which a quasi-scientific method is seized upon, even though the originator may reject the purpose to which it is put.
Taylor’s use of bullet diameter, instead of cross-sectional area, is in fact mathematically incorrect, as a bullet having twice the diameter to a smaller one has in fact more than twice the cross-sectional area.
Momentum and “stopping power”
There is another bunch of armchair ballisticians that favour the use of momentum (in isolation) being a good measure of stopping power. I admit to having been one of these because the thought behind it seemed to lend more credence to the performance of lower-velocity, big-bore cartridges than what the kinetic energy story told. It is demonstrated that arguments made by this theory in support of “stopping power”, turn out to be just as weak as those in support of kinetic energy in isolation, which we will look at presently. The only time that momentum appears to hold a measure of validity is if a heavy bullet of .577 or .600 Nitro Express (or larger) passes close to an elephant’s brain through the spongy skull surrounding it. The impact of this blow in some cases can stagger the animal.
Problems with this theory are indicated as the following:
- Momentum on its own as an indicator of “stopping power” is meaningless if bullet construction and other factors are ignored.
The following example is presented which exposes the fallacy of momentum on its own being an acceptable indicator of stopping power:
You have a three-pound spear traveling at 50 fps and a three-pound gel-filled bag traveling at the same velocity. They have equal mass and momentum. Which one would you prefer to be hit by? Logic soon identifies which object is likely to be the most lethal without having to resort to field testing! It is also rather interesting to note that the momentum of the above two projectiles is almost identical to that of a factory-loaded 500-grain .458 Winchester Magnum. Do you possibly think that an elephant or buffalo would be staggered by the impact of a three-pound gel-filled bag thrown at it at 50 feet per second? The answer is self-evident. See Figure 2.
Clearly momentum theory on its own falls way short of reality, so this formula can also be filed away in the redundant folder.
Threshold of wounding potential based on kinetic energy
This theory implies that the more kinetic energy a bullet possesses, the more stopping power it has, and the quicker it will dispatch an animal – i.e. Ek=1/2mv2
Why does this formula not hold water?
Kinetic energy on its own as an indicator of “stopping power” is meaningless, because bullet construction and other factors are ignored. Consider two bullets of the same calibre (say .308 Winchester for example) and mass. Bullet A travels at 50 feet per second faster than bullet B. Bullet “A” (a non-expanding bullet) may have more kinetic energy, according to the formula, than bullet “B” (an expanding soft point), but if the construction of bullet “A” is of such a nature that there is no expansion, and it drills right through the target creating a very narrow wound channel, it is likely that the animal will run off and not expire very quickly. If bullet “B” holds together, and mushrooms well to create a wide and deep wound channel, it will drop the target animal quicker than bullet “A”.
Because a quantity of kinetic energy is not, in and of itself, sufficient to adequately describe the wounding characteristics of a bullet, does not imply that kinetic energy is not a valid measure of ballistic performance. It is, but not on its own, because there are other variables which have to be factored into the equation.
We also know that when we drive a bullet at very high velocity the probability of it breaking up on impact and causing a shallow (non-lethal) cratering wound is increased. If we take that same bullet (same mass), and drive it at a lower velocity (which will equate to a lower kinetic energy), we will reach a point where we will have good penetration which will result in a greater effect on the target.
Optimal Game Weight (OGW) formula
First appearing in the April 1992 issue of GUNS magazine, the OGW formula was reported to be the result of careful experimentation taking the various contributions of kinetic energy, momentum, bullet sectional density, bullet diameter, bullet nose configuration, and a number of other criteria into consideration.
The author did not elaborate on his experimental methodology, but came up with the following formula:
OGW (lbs) = Velocity (fps) 3 x Bullet weight (grains) 2 x 1.5 x 10-12
The weakness of this formula is soon exposed when the following are considered:
The OGW formula is nothing more than kinetic energy multiplied by momentum, then multiplied by some constant to arrive at the desired weight range.
There is nothing magical about the answers presented by this formula. It is based entirely on the result of a subjective choice of the constant (i.e. 1.5 x 10-12), divided by the acceleration due to gravity.
The OGW formula does attempt to combine the separate contributions of kinetic energy and momentum, but however well-intentioned this may be, multiplying the two values together is not an unacceptable method of deriving a composite effect. The following illustrates why this is so:
An 85-grain .243 calibre light game bullet with a velocity of 3500 fps. has an OGW rating of 389 pounds at the muzzle. A 575-grain ball traveling at 850 fps has an OGW rating of 305 pounds. The former bullet is appropriate for small, light, and thin-skinned game and the latter is “to stop charging tigers”. The OGW has little application to reality.
Although the author mentioned taking “kinetic energy, momentum, bullet sectional density, bullet diameter, bullet nose configuration, and a number of other criteria” into consideration, the effects of sectional density, bullet diameter, and nose configuration appear nowhere in the formula, and bullet construction is glaringly neglected in the article.
By making velocity a third-order term, it wildly exaggerates the effect of this component in terminal bullet behaviour, which has surprisingly little effect on deforming bullets.
Another formula bites the dust.
“Energy dump”, “over penetration” and “hydrostatic shock”
The basis of these somewhat similar theories is that a bullet, which remains inside a target, is more effective (in terms of stopping or killing power) than one, which completely penetrates and passes through because all the energy is “dumped” into the target. If it passes through, the residual energy still contained within the bullet is wasted (see Figure 3). If the energy is not wasted on exit, it is deemed to have been more effective by having exhausted itself entirely on the target animal.
What’s wrong with this theory?
If a bullet “over penetrates” (comes to rest under the skin on the opposite side of the entry hole), or passes right through, ineffective “stopping power” is not due to wasted energy, but “under cavitation”. In other words, the wound channel created by the bullet (i.e. the cavity) must be of sufficient diameter to cause enough damage to vital organs.
It makes no difference then if the bullet passes partially or right through the target, as long as it penetrates enough to reach vital organs. Wasted energy is irrelevant if the wound channel is of sufficient diameter being a wound track of 0.75 – 1 inch in cross-section (19 -25mm) through the heart, lung, or major arteries.
If one considers a bullet that enters the target, does not exit, dumps all its energy but fails to hit any vital organ along the wound track, all the energy of the bullet may have been expended on the animal, but it is likely, despite the “energy dump”, to still run off and take a long time to die.
From the standpoint of efficiency, the ideal case would be when a bullet penetrated enough to barely exit the opposite side. However, this is a distinct difference between efficiency and effectiveness.
Most experienced hunters prefer an exit wound as it leaves a better blood trail.
The rate of energy transfer is vastly more important than the quantity of energy transferred.
It is not the energy itself that kills; it is the character of the work done by it.
There is no such thing as “hydrostatic shock”. The energy pulse originating from a bullet entering the watering medium of living tissue is not static. It moves and is therefore dynamic.
Lethal Index formula
John Wooters the well-known gun writer, frustrated by the litany of kinetic energy figures, suggested a formula that, he believed, was a more reliable indicator of a bullet’s effectiveness on live game. Unlike the Taylor Knock Out rating, the Lethality Index (or L factor) is intended to be a measure of effectiveness on thin-skinned game by expanding rifle bullets:
LI=Kinetic energy (ft. lbs) x Sectional Density (SD) x Bullet diameter (inches)
This theory is questionable for the following reasons:
Large calibre bullets admittedly do make bigger wound channels than small calibres, kinetic energy is a valid component in the measure of wounding, and bullets with a high sectional density penetrate deeper and expand without coming apart (all things being equal). But, all things are not on an equal footing and this formula, like others that don’t even take bullet performance into account, cannot be considered a meaningful measure of terminal effect.
This formula is an assessment of the potential of a specific cartridge-load combination and its components at the muzzle. Downrange performance of otherwise identical loads can be very different and that sectional density, in particular, is an unreliable indicator of bullet performance.
And so RIP (Rest in Peace) Lethal Index Formula.
Knock-Out Value (KOV) formula
This formula was invented by a South African by the name of Chris Bekker and is based on a simplified, but slightly erroneous, “terminal momentum” calculation:
KOV = “Terminal momentum” (lb. ft/s) x Sectional Density (S.D) x “Mushroom factor”
Where:
Terminal momentum = Impact velocity (fps) x Retained bullet weight (lbs)
and
Sectional Density = Original bullet weight (lbs) / Bullet diameter (inches)
At first glance, this formula appears to be moving in the right direction but fails on closer scrutiny.
- Why should it be “terminal momentum” multiplied by sectional density? Why not kinetic energy multiplied, or divided by, expanded frontal area, for instance? From where did this insight arise?
- Where is the physical evidence justifying a “Mushroom Factor”, and who decides on the value of this arbitrary factor?
The only evidence that the author presents to support the validity of his theory is in the form of comparisons to other “indices” and “factors” or to kinetic energy alone. No documentation or analysis is provided to show how these relationships in the KOV were derived. When the support of field evidence is drawn upon for evidence it is entirely subjective. This sort of reasoning does not qualify as scientific argument or evidence.
None of the mathematical dexterity demonstrates anything other…. than to satisfy one’s preconceived notions about how things are expected to work.
Pseudo-science
What is the root cause of all this erroneous ballistic misunderstanding? The author of the article justifiably lays it at the door of pseudo-science. He points out that “to be meaningful and scientifically sound (correct and true), a formula or theory must be founded on carefully collected test data, not “gut feelings”, prevailing perceptions, and anecdotal evidence (which is little better than hearsay).
Scientific, analytical, methods and measures must be as objective and quantitative as possible. Consequently, theories of terminal effects of bullets must be evaluated in quantitative terms, meaning that dimensions of wounds must be evaluated, and together with a host of other factors, be taken into account. None of the formulas discussed in this article can be quantitatively defended with a study of field results– there are too many anomalies and variations to be explained away.
Field experience, without carefully planned scientific record taking and analysis, is almost useless. Science is founded on fact which can be examined and tested by any individual. Unfortunately in the hunting world, there are many pseudo-scientists. People like myself who have intense interests in ballistics, but who are not scientifically trained ballisticians, often come up with subjective theories, which somehow take root and become accepted as “gospel”.
Unfortunately, terminal ballistics is a lot more complex than what we would like it to be. So many of the theories and formulas that have been suggested have been oversimplified, because they have been put forward by individuals, some of whom admittedly may have extensive field experience, but have no formal scientific training in the field of ballistics in which mathematics, involving complex calculus and differential equations, are the order of the day.
Then again, there may be trained ballisticians who have little knowledge of anatomy and physiology, and the response of a body to the effects of a bullet. There are so many variables, and to neglect even one or two would provide answers that are not a reflection of the truth.
Let us just for a moment list some of the variables involved in how a bullet performs on contact with, and entry into living tissue, and what these mean in terms of a bullet’s knockdown performance, stopping power, lethality index, or whatever term equates to how quickly and efficiently it can kill an animal.
Looking first at the bullet and its terminal performance, here are some of the variables that come to mind (there are likely to be many more that I may not have taken into consideration):
- The dimensions of the bullet (length and diameter) and changes that might occur as it is passing through living tissue, e.g. increasing diameter in expanding bullets.
- Its impact mass and mass through the target (which will progressively decrease, and be largely determined by its ability to stay together, and influenced by the types of tissue encountered along the wound channel).Its impact velocity and velocity through the target (which will progressively decrease and be influenced by the types of tissue encountered along the wound channel).
- Its rotational energy and momentum at the point of impact and through living tissue.
- Its impact momentum and momentum through the target (which will progressively decrease and be influenced by the types of tissue encountered along the wound channel).
- Its impact kinetic energy and kinetic energy through the target (which will progressively decrease and be influenced by the types of tissue encountered along the wound channel).
- The shape of the nose (angle of the ogive, ball, spitzer, flat nose etc.) and how it may change as it passes through living tissue).
- The incident angle (i.e. the angle of the bullet as it impacts the target animal) – yawing, tumbling, flying straight, etc.
- Rate of energy transfer.
- Effect of the bullet caused by the density of tissue at the initial point of contact and along the wound channel.
- The cohesive properties of the bullet (i.e. its ability to stay together and not break up) which will be determined by its construction
- Soft nose, ballistic (plastic) tip, monolithic or FMJ construction.
And now let us for a moment consider the animal variables, which will affect the bullets performance:
- The diameter and depth of the wound channel (there may be more than one if the bullet breaks up)–it may vary in size along the path of the bullet.
- The path followed by the wound channel and structures encountered along the way. The diameter and path along the wound channel, as well as the number and type of vital structures destroyed or damaged along the way, will largely determine how fast the animal will lose blood, go into circulatory shock, or have the central nervous system disrupted and die.
- The condition of the animal at the time of being shot (i.e. state of health). An animal in poor, weak or debilitated condition is likely to be more susceptible to the affects of a bullet.
- Nutritional status of the animal at the time it was shot.
- Mental state at the time of being shot. If in an excited state with high adrenaline levels, it may deal more efficiently with the shock resulting from being hit by a bullet.
- Blood pressure.
- Blood volume.
- Rate of blood loss.
- The rate at which living tissue, such as skin, connective tissue, muscle, tendons, ligaments, and bone resist the passage of a bullet.
- The animal’s ability to compensate for blood loss (i.e. the compensatory phase of shock).
- Respiratory and cardiac function.
And so on…
The point I am trying to make here is that there are so many variables involved, that none of the existing formulas come anywhere near to forecasting the predicted outcome a bullet will have on any given animal, assuming that the bullet arrives at its point of contact without having being deviated along its course from the muzzle by crosswinds, or having made contact with a twig or other object.
I have read carefully through the work of the unknown ballistician and found it to be accurate, consistent, reliable, credible, and well up to the test of scrutiny, and am in total agreement that none of the formulas we have been presented with to date, and which most of us have readily propagated, come anywhere near to accurately predicting the terminal performance of a bullet on a living animal.
And so for us who are fascinated by how projectiles fly and perform, it is time to rethink things that we have so gullibly accepted in the past.
References
Aagaard, F. Big Bore Rifles. Anon. Shooting holes in Wounding Theories: The Mechanics of Terminal Ballistics. Taylor, J.P. 1948. African Rifles and Cartridges. Stackpole Books, Harrisburg
