... Though never ideal--and ultimately in a sense an "abstraction"--i like the idea of "measuring" via the "Taylor KO Formula" for a KO value.
Velocity X Weight X Diameter divided by 7000 = KO value.
Some general comparisons below, based on approximate velocities with commonly used pill weights:
.22 Long Rifle: 1.5 KO value;
.32 ACP: 2.75 KO value;
.380 Auto: 4.7 KO value;
9 MM: 7.0 KO value;
.40 S&W: 10.0 KO value;
.45 ACP: 13.3 KO value;
.44 Magnum: 18.0 KO value;
They are only "numbers", "abstractions", but if we can accept them in this light the results are made manifest, and individual handgunners must decide for themselves.
Sorry, but the KO really is absurd. It arguably doesn't even work for it's intended purpose, but it's intended purpose by Taylor was only to judge the effectiveness of solid rifle bullets on elephant skulls:
http://www.rathcoombe.net/sci-tech/ballistics/myths.html#tkoI just calculated the KO for a standard softball thrown at 50 mph. It is 384.98. This would make a 50 mph softball 55 times more effective than the 7 KO value of a 9mm. Probably not credible. It gives way to much emphasis on diameter. Because Taylor came up with it, so many people, including gun writers, have latched on to it. But it doesn't even do what Taylor wanted, and Taylor never intended it to have anything to do with hollow-point handgun bullets in self-defense on human targets.
Some of these types of answers can only leave a person to scratch their noggin.
Any "calculation or formula", whether it be foot pounds, Taylor KO, relative incapacitation index, etc., are merely abstractions, simply "yardsticks" used for some means to compare--no matter how absurd or crude they may appear to be.
We're talking here about projectiles--from 40 grains to 240 grains--launched from firearms--traveling at velocities from 900 fps to 1250 fps.
I've heard the softball, snowball, and shot put comparisons all before--and though (foolishly), they can be assigned a Taylor KO number, it's utter foolishness to equate a hand launched softball to a firearm launched projectile.
The proof would be in the pudding: no person who sets forth this argument (or any person for that matter), would go out and hunt black bear, deer, elk, or moose--or, within a city setting--face down a goblin intent on doing bodily harm--with a softball as a projectile of preferred choice. Using comparisons such as these is a thousand times more absurd and crude, than any formula devised by others to try and compare the "stopping abilities" of specific cartridges.
In a perfect world we'd do away with all of these "calculating methods", but until then...
There is a reasonable debate as to the relationship of the kinetic energy of a bullet and its terminal effect. It obviously depends on bullet construction, the dimensions and construction of the target, etc �
But kinetic energy has been around since � forever. It wasn�t invented. It is a scientific concept. Unlike KO, it was not invented recently. Although it involves two components, rather than one component, it is a scientific concept that that has been around since the universe expanded, and certainly before firearms were invented. It�s just like velocity or mass itself.
KO was, on the contrary, a human invention to try after the fact to justify the effect of larger caliber solid bullets at rifle velocities on a very narrow range of mass/velocity and on a very narrow scope of African targets. It doesn�t even do that well, but it certainly doesn�t have, and never was intended to have, any application to 9mm hollow point rounds.
This guy is skeptical of the correlation between KE and wounding, but he acknowledges the fallacy of comparing it to other made-up formulas:
S]imply because an arbitrary quantity of kinetic energy is not, in and of itself, sufficient to describe the wounding characteristics of our weapons does not imply that kinetic energy is not a valid measure of ballistic performance. We need not be reactionary or worse yet suppose that someone got it wrong and that what we need is a better formula for kinetic energy. This truly novel and disturbing misconception was once highlighted in a feature article, the essence of which was that kinetic energy is simply the arbitrary fabrication of some gun writer, not based on physical laws, and is fundamentally incorrect.
Reading something like this, its as if the cancerous pseudoscience of gun writers has spread to corrupt even the hallowed precepts of true science. I shouldn't make it seem as if the author of this particular article were alone in his assumptions. The history of popular terminal ballistics in the 20th century saw several examples of this kind of crackpot science, such as Elmer Keith's ridiculous invention of "pounds-feet". What is most astounding about particular outrage against science and clear reasoning is that the (long since departed) editors of the magazine didn't know enough themselves to prevent its publication. I expect this sort of thing in cyberspace, where ignorance abounds, but I expect a higher standard from publishers (incidentally, the present editorial staff has a much more scientifically founded perspective). Men like Townsend Whelen knew their basic science and would not have made such errors, nor permitted them to be published in their journal. It troubles me that our knowledge has diminished so much in 70 years.
When gun writers attempt to describe terminal ballistics in terms more technical than "wallop" they take on the mantle of science and bear the responsibility to their readership to convey an accurate discussion of the mechanisms involved. Science does not merely belong to scientists nor only in the realm of the scientific journal. It is truth on a fundamental level. There are no "everyday" meanings to terms such as velocity, momentum, kinetic energy and impulse. They are not slang or jargon used to describe nebulous, ill-defined concepts. They hold precise meanings. To carelessly misuse scientific language is to render a disservice to the readership, even though it be predominately composed of non-technical readers.
Before going any further let me make an apology to the reader. This article and the letter exchange is now ancient history. It was not my intent then nor is it now to pillory anyone. I wrote my own letters to the editor of the magazine at the time in hopes of inspiring a more fastidious editorship in terms of technical matter. I feel justified in rehashing the argument in cyberspace because it represents a viewpoint with which I suspect many reasonably educated shooters would sympathize - and I don't mean my viewpoint! I understand that much of what I am pressing here seems arcane and unimportant to most shooters. But the integrity of such concepts is the fundamental underpinning to all ballistics, the technology on which we depend. Is it necessary for the average shooter to understand all these concepts and be thoroughly conversant? No, it is not. However, when they are discussed, the discussion needs to be scientifically correct.
I guess I expect too much and perhaps I am being too critical, but whether the average Joe understands the ins and outs of physics is not the issue - its the attitude that accredited science is no better than hip-pocket hooey that bothers me. Its the attitude that science is based on opinion, rather than fact. Its the same mentality that has lead to the wholesale disrespect of science in America, and that has allowed a culture to flourish with notions such as New Age mysticism, literalist religious extremism trumping science in the classroom and denial of global warming despite undeniable evidence.
Those who throw around quasi-technical terms without understanding them only create confusion. Velocity is not impulse. It is not like impulse. Kinetic energy is not momentum and velocity "combined". Momentum will not describe "the load with the hardest thump". There is no room in true science for a private opinion about a better definition of energy, and those who ask "Is the ft-lb an accurate KE label?" should not be published.
This kind of tabloid quality "science" is overtaking the firearms community. In the age of bioengineering, quantum electronics and relativistic physics, the firearms community is becoming mired in a level of scientific ignorance comparable to Medieval Europe. The truth is not marketable but crackpot theories about better formulas for kinetic energy warrant feature articles. Falsehood and error need to be corrected. Those of us who care about the quality of the literature and the accuracy of the inquiry into terminal ballistics bear the responsibility to repudiate the nonsense and to authoritatively instruct concerning the facts.
Since this has proved to be a pitfall for some I will unravel the mystery. The definition of energy is based upon physical laws. A ft-lb is a valid unit of kinetic energy - by definition. There is nothing to prove. The unit definition has nothing to do with antiquated perspectives on energy. Kinetic energy is calculated as (1/2) mass times velocity squared. But pounds are actually a unit of force (i.e., weight), which is mass times acceleration (due to gravity in this case). So, to get kinetic energy we must divide by 32.174 ft/s2, which reduces the velocity squared terms of ft2/s2 simply to feet. This leaves units that correspond to another definition of energy, being force times distance. Its really only confusing in the old English system of units because we normally think of pounds as mass rather than as force; in metric its obvious that all forms of energy are the same thing because they are all in Joules or kg-m2/s2.
Just in case somebody doesn't know, foot-pounds are a real quantity and can be converted into BTUs, Joules, kilowatt-hours, calories, ergs, electron-volts or any other measure of energy as you please. All of these resolve down to the same fundamental quantities of mass times distance (divided by time) squared. Not all energy is the same, but all energy has the same fundamental units. Kinetic energy was not invented for the delight of gun writers. The different definitions of energy are based upon inter-related physical laws, none of which have been overturned since God created the universe, let alone in the last century.
Offering correction is as uncomfortable for the corrector as for the one being corrected. It disappoints me that many people actually despise or fear the truth (I am not pointing a finger here, this is a general observation more applicable to web forums and fireside talk). It is a subtle thing, typically taking the form of a resistance to let go of cherished misconceptions and an egoistic tendency that we all share to be knowledgeable. I have been proved wrong many times in my life and while the experience is not always a comfortable one, I am happier for being corrected. Not everyone is made happier by correction.
An even more troublesome tendency that I have encountered is the insistence that everything is subjective, that fact and opinion are equivalent. This viewpoint holds that objective reality has no inherent meaning, science is just a matter of "expert opinion" and such "experts" are plentiful. If, as some have contended, all measured data such as penetration depth and wound diameter (even in game animals) provide us no absolute knowledge, if any degree of uncertainty removes all hope of understanding, then truly we have embraced superstition (or a weird form of agnosticism) and are equally well served by consulting an astrologer about the performance of our weapons.
KE does not necessarily predict the effect on a particular animal of a bullet, because of material issues of bullet construction, the size and construction of the game (a more violently-expanding bullet may do better on a smaller animal (e.g., a human) but when extreme penetration is needed on some giant animal you might want a solid; etc... Also, some of the KE is converted to heat energy, etc ... But energy is an inherent scientific concept. It's just like mass and velocity. KO is just a made up thing.
Again, it has its limitations, but KE says that a 50 mph softball has 1/6 the effect of a 9mm. KO says it has a 55 times the effect of a 9mm. KE is at least a starting point. KO is just silly.