Taylor Knock Out Factor

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Obviously, the issue is complicated by such ideas as overpenetration, size and weight of the handgun, shot-to-shot recovery times etc., but on the whole, I lean toward the most powerful round I can carry.

My too. I've been thinking about this quite a bit recently.

I cannot fire 6 shots of .44 Magnum from my Redhawk rapidly without needing to adjust my grip. Therefore, this is too much power for me to be able to handle for self defense (probably even for bears if I'm being honest with myself).

But I can do that with .357 Magnum in a medium frame double action, or 10mm in a G20. And can also shoot them both one handed repeatedly without needing to adjust my grip. That is an acceptable level of control to have over the firearm, imo. So rather than look at what gun/cartridge combo I can shoot the absolute fastest, I'm currently exploring the threshold on the high end of the range where I am losing controllability of the gun.

To the OP: I briefly looked at the TKO concept, and turned away. It just doesn't make much sense to me. If I had to pick a single metric to put my faith in when choosing a handgun cartridge, it would be muzzle velocity. I like the number 1250fps.
 
I have the book. It is an interesting read from the personal perspective of a guy in the bush shooting lots of big critters for their tusks many years ago.

Like when I read Horn of the Hunter, Sixguns, No Second Place Winner and several other classic gun works, the info is interesting. But in all honesty, today it is pretty much outdated stuff.

Stay safe.
 
My too. I've been thinking about this quite a bit recently.

I cannot fire 6 shots of .44 Magnum from my Redhawk rapidly without needing to adjust my grip. Therefore, this is too much power for me to be able to handle for self defense (probably even for bears if I'm being honest with myself).

But I can do that with .357 Magnum in a medium frame double action, or 10mm in a G20. And can also shoot them both one handed repeatedly without needing to adjust my grip. That is an acceptable level of control to have over the firearm, imo. So rather than look at what gun/cartridge combo I can shoot the absolute fastest, I'm currently exploring the threshold on the high end of the range where I am losing controllability of the gun.

To the OP: I briefly looked at the TKO concept, and turned away. It just doesn't make much sense to me. If I had to pick a single metric to put my faith in when choosing a handgun cartridge, it would be muzzle velocity. I like the number 1250fps.

I am in the process of switching from a K frame .357 to a Glock 29 - the subcompact 10mm - with a dot. It will be interesting to see if I can control the recoil. I like the horsepower, but I'm worried about putting it into the ceiling.
 
I am in the process of switching from a K frame .357 to a Glock 29 - the subcompact 10mm - with a dot. It will be interesting to see if I can control the recoil. I like the horsepower, but I'm worried about putting it into the ceiling.

If you can keep a solid grip - and if you shoot .357 from a K frame, I bet you can - I don't think you'll have a problem. ;)
 
But, can we all agree that the most often stated simple ft pounds of kinetic energy is very limited? It seems not to capture the true efficacy of the round.
There is no single number that's going to provide significant insight into the complete terminal effect of a bullet on living creatures.
 
There is no single number that's going to provide significant insight into the complete terminal effect of a bullet on living creatures.
But if you have the information needed to calculated kinetic energy, you are working with more than one number and you lack only bullet construction (geometry and material properties) to have a complete picture of the projectile and its potential. There is not much more you can know about the bullet (velocity, geometry, material properties) other than Ballistic Coefficient (a model for drag as a function of velocity). In theory BC or the drag function itself can be calculated from first principals (geometry) but in practice is most often done empirically from radar data.

My final thought on Kinetic Energy. Kinetic Energy is the only energy a bullet brings to the terminal event (unless it has an energetic payload). If the bullet does any work on itself or the target it does this by turning its kinetic energy into whatever the resulting work is (noise, vibration, heat, elastic or plastic deformation of the bullet or target etc). The bullet's geometry and material properties can have huge effects on what and how efficiently the kinetic energy is turned into other work but the kinetic energy the bullet has at impact is a hard limit on how much work the bullet can do to itself and/or the target.

-rambling
 
There is no single number that's going to provide significant insight into the complete terminal effect of a bullet on living creatures.

I would say “zero”, would be accurate to describe the terminal effect on “living” things. :)
 
...the kinetic energy the bullet has at impact is a hard limit on how much work the bullet can do to itself and/or the target.
Correct. Unfortunately, that isn't nearly enough to provide the information people want to know. Think of it like this. Imagine a weapon that will destroy exactly 1% of an aircraft carrier with a hit. Now with that precise quantification, tell me what the effect of firing the weapon at the aircraft carrier will be. Will the aircraft carrier be disabled? What capability will it lose? How long will it take to repair from the damage? The problem is that it's not enough to know how much damage the weapon CAN do or what percentage of the carrier is destroyed, it's far more important to know what was hit.
I would say “zero”, would be accurate to describe the terminal effect on “living” things.
The study of firearm ballistics is traditionally broken down into three main category. Internal ballistics (what happens inside the gun), external ballistics (what happens between the gun and the target) and terminal ballistics (what happens when the bullet hits the target).
 
Yeah, if it’s still alive and running around after it’s been hit, try something else.

I tried lots of stuff before I found something that worked well in 300 blk. Construction made more difference than the slight FPS / bullet mass differences between the winner and all of the loosers.
 
Yeah, if it’s still alive and running around after it’s been hit, try something else.

I tried lots of stuff before I found something that worked well in 300 blk. Construction made more difference than the slight FPS / bullet mass differences between the winner and all of the loosers.

This is where that kinetic energy can be somewhat insightful within constraints (ie other numbers & data). 300 BO has a relatively low Kinetic Energy potential for a 30 caliber cartridge and thus is highly dependent on selecting a good bullet to efficiently use that energy to accomplish the job (I am assuming you're hog hunting). If you had stepped up to say 308 Win or even 300 Win Mag or 300 Norma Mag that shares the same caliber and bullet availability do you think those higher kinetic energy 30 caliber cartridges would have been as picky about matching a satisfactory bullet to the job?

In my experience the increased kinetic energy (in a given caliber) usually increases options and margins but not without some pit falls and down sides.
 
No one who has an understanding of terminal ballistics. To understand my statement, use the Taylor formula to calculate the "Knock Out Factor" of a 16lb bowling ball rolling down an alley at 24.5 fps vs a .45 ACP.
Bowling ball:
Mass (in grains) - 112,000
Velocity - 24.5 FPS
Diameter - 8.5"

Bowling Ball - 332.2 Taylor Knock Out Factor ((112,000*24.5*8.5)÷7000)
.45 ACP - 15.2 Taylor Knock Out Factor

According to Col. Taylor's theory a bowling ball rolling toward the pins has more than 20 times the knock out capability of a .45 ACP.

I'd prefer to lay down on an alley and let someone roll a bowling ball at me than let someone shoot me with a .45.

I get what you are saying, but you are applying the TKO formula out of context. The formula was developed to compare rifle cartridges and the impact of bullets on large game.

In the Buffalo Bore article I linked to, the author (Tim Sundles) used two cartridges to demonstrate the difference between using the standard energy formula with the TKO formula. The cartridges, 22-250 vs. 45-70, had very similar energy levels, but totally different TKO results, showing their hunting applications on big game.
 
If you had stepped up to say 308 Win or even 300 Win Mag or 300 Norma Mag that shares the same caliber and bullet availability do you think those higher kinetic energy 30 caliber cartridges would have been as picky about matching a satisfactory bullet to the job?

Actually, I already use/have used those calibers and the bullets they do fine with were a “no go” with the 300bo (other lighter for caliber bullets too). I was about to give up with it working well at all until you suggested the TAC TX bullet, really made the round something useful vs a disappointment. Use it almost every weekend now.
 
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The formula was developed to compare rifle cartridges and the impact of bullets on large game.
It was much more specific than that.

It was intended to estimate provide relative information about how long an elephant would be knocked out if hit in the skull, but not the brain, by a bullet from a particular rifle cartridge.

No one ever suggested it had anything to do with handguns or general prediction of terminal effect of rifle bullets until some gunwriter(s) realized that it appeared to support pet theories on stopping power and co-opted it for that purpose.

1. It does not relate to any scientific property of projectiles.
2. It was never intended to predict anything about handgun terminal effect.
3. It was never intended to predict anything about the general terminal effect of rifle cartridges.

The bottom line is that you might as well make up your own measure of terminal effect and use that to compare handgun cartridge terminal effect instead of TKO. Maybe take the year of invention of the cartridge times the overall length of the cartridge in millimeters times the maximum average pressure times the bullet weight. Something like that has just about as much chance of providing useful information as the TKO.
 
TKO formulas are made for solid, hardcast type rounds, not for hollow points.
TKO measure Kinetic Output(energy drop) potential as an increasing number.
There is no perfect formula for hollow points as they are all constructed different, but in general, when the hollow point expands it increases its "TKO" also reducing its sectional density, which brings it to a stop faster. TKO is the math behind hollow points.
When it comes to hollow points for defense from people, 12"-18" in gel is what needs to be looked at because it can be achieved with almost any caliber depending on the bullet construction.
When you get into hardcast rounds, TKO is just s measure of what we already know, a fatter bullet will stop faster, and, like an expanded projectile, will create a bigger wound track and more tissue disruption and less penetration.
We know a FMJ is not as effective as a hp on human because it does not expand, over penetrates and will not dump all its energy in the target making it a zip through that will hardly be felt by a crazed attacker.
When using FMJ or solid hardcast projectiles the bigger bullets have the advantage against aggressive attackers, human or not. For precision shots in hunting, smaller calibers are ideal with more penetration to reach the vitals you are aiming for.
For SD against large animals, bigger calibers for more pain infliction, tissue disruption and bone damage.
 
Lets look at the formula for TKO

TKO = mass/weight (lbs)* x velocity (fps) x diameter (inches)

*The formula is some time shown with weight in grains but then the whole equation is divided by 7000 which in the conversion from grains to lbs. I sometimes also see it referenced as mass but both grains and lbs are units of weight/force not mass.

First thing we have to notice is the units are not consistent. The velocity and dimeter should be using the same length unit, ie if we are using velocity in fps than bullet diameter should be in feet. If we are doing bullet diameter in inches then the velocity should be in inches/second.

If the formula really meant mass then in the US customary units it would be in Slugs (or Pound-Mass for you youngins), On earth 1 Slug of mass set on a scale would weight 32.174 lbs (F = ma where a is acceleration and in this case due to gravity 32.174 ft/sec^2). For this discussion that mostly become a scaling issue assuming we are only shooting earth critters. :D

But if Taylor had actually meant mass not weight... Mass x Velocity is classically Momentum and that is an important property of a body in motion. But the multiplication by diameter is where we depart from a quantity commonly used in engineering or physics.

The resulting units of TKO are lb-(ft/sec)-in. If we assume the lb was actually suppose to be mass and we convert one of the lengths into the other (ie velocity in inches/sec or the diameter in feet) we would have a number with units that looks like Angular Momentum. In US customary Angular momentum is often shown with the units of slug-in^2/sec but that does not make any physical sense in this application just a bit of metal gymnastics with units.

-rambling
 
Does anyone else calculate the Taylor Knock Out Factor when looking at loads and different cartridges.
It may be fun to look at your favorite loads or start an argument, but it should be a fun discussion :cool:
Nope, not at all...

DM
 
the kinetic energy the bullet has at impact is a hard limit on how much work the bullet can do to itself and/or the target.

This is true - but it isn’t, because that “hard limit” of Kinetic Energy can never even be approached by the Work done in this real world system.

In inelastic collisions - as in ALL COLLISIONS IN THE REAL WORLD, Kinetic Energy is NOT conserved. However, MOMENTUM, in fact, IS conserved. So quite literally, impact MOMENTUM is the hard limit for defining the Work which can be done by a bullet.

Let’s get real for a second though. Taylor KO Factor is Momentum times bullet diameter. Kinetic Energy is Momentum times half of muzzle velocity. At their core, the two aren’t so different, but rather only prioritize one additional factor compared to that prioritized by the other. I wrote a blog many years ago and evaluated a dozen or so various “metrics” like TKO, Hornady HITS, KE, Bohr factor, etc and not surprisingly, they’re all built upon velocity times bullet weight (momentum) - then multiplied or divided by whatever other factors they choose to emphasize, whether it is weight, bullet diameter, expanded diameter, velocity, etc. based on whatever preference the author of each particular formula might prefer.

In that regard, TKO really has just as much merit as any other numeric metric we might choose - and frankly, MORE merit than do many of them, including Kinetic Energy.
 
Everyone always brings up Taylor. There is also Hatcher RSP, and Thorniley, both come up with similar results to TKO.
 
Here’s a copy of a summary I posted here 5yrs ago as a comparison of several metrics of stopping power, analyzed for what variable they value or devalue. You can see from each formula, they’re all just a pile of diameter, bullet weight, and velocity, multiplying or dividing by each in various ways as the author saw fit to favor or devalue whatever they thought was most important:

varminterror said:
Kinetic Energy
KE = M * V^2 / 450380 (which is 1/2MV^2 converted for gravity & pounds)
~Momentum x velocity <-- Strongly values velocity, values mass

Taylor Knock Out Factor
TKO = M*V*D/7000
~Momentum x Diameter <-- values bullet weight, velocity, and diameter equally

Thornilly Stopping Power (Have seen "thornilly” spelled 3 or 4 different ways)
TSP = 2.866 * V * (M/7000) * sqrt(D)
~Momentum x sqrt(Diameter) <-- values bullet weight & velocity equally, SLIGHTLY values diameter

Hornady HITS (Have seen 2 different formulas for this one)
HITS = V * SD * M/100 = M^2 * V / D^2 / 700,000
~Momentum * Mass / Diameter^2 <-- Strongly values mass, values velocity, strongly devalues bullet diameter

Wooter's Lethality Index
LI = KE * SD * D = M^2 * V^2 / D / 450380
~Momentum^2 / Diameter <-- Devalues diameter, strongly values momentum (mass & velocity equally)

Optimal Game Weight
OGW = V^3 * M^2 * 1.5x10-12
~Momentum^2 x Velocity <-- Very strongly values velocity, strongly values mass, velocity moreso than mass

Bekker Knock-Out Value
BKOV = impact velocity * retained bullet weight * SD * Mushroom factor
~Momentum x retained mass x expansion ratio / Diameter^2 <-- Strongly devalues bullet diameter, values velocity & expansion, strongly values mass (mass * retained mass), values mass overall

Hatcher Relative Stopping Power
RSP = M * V / (2 * G) * A * F
F - Form Factor 700 - 1350 based on bullet shape & expansion
A = pi * D^2 / 4
~Momentum / Gravity x Diameter^2 * Form Factor <-- Values form, expansion (within form factor), weight, & Velocity equally, highly values diameter, diameter overall

Power Factor
PF = M * V / 1000
~Momentum <-- Values mass & velocity equally
 
You can see from each formula, they’re all just a pile of diameter, bullet weight, and velocity, multiplying or dividing by each in various ways as the author saw fit to favor or devalue whatever they thought was most important:
The big difference is that momentum and kinetic energy don't have "authors". They were discovered via scientific experimentation, not made up by someone trying to favor or devalue certain factors based on their perception of what is important and what is not. They are established scientific properties of moving objects, not someone's idea of how to rank ammunition effectiveness.
 
You can call it whatever you want of course - the originator of the term is long dead - but TKO is one of the most misused firearms "formulas" extant. Most will think: John Taylor shot a lot of elephants - he's GOT to know what he's talking about! Well, he does. Unfortunately, what he talks about regarding TKO has little to do with handgun (or rifle) hunting game with expanding bullets:

"I do not pretend that they [TKOs] represent "killing power"; but they do give an excellent basis from which any two rifles may be compared from the point of view of the actual knock-down blow, or punch, inflicted by the bullet on massive, heavy-boned animals such as elephant, rhino and buffalo". (African Rifles and Cartridges, pg. xii)

Not quite what most shooters THINK he said, is it? For those who bother to actually read what Taylor had to say, it is clear that his TKO formula only applies to the knockdown ability of headshots into large African game with non-expanding bullets. <snip>

Your Taylor quote didn't say anything about head shots, but you did. (was part of the quote missed?)
 
As we discuss different measurements I think we need to look at the whole instead of one part.
SD is a good tool for determining penetration and when evaluating bullets for a given cartridge. But not necessarily the effects on a game animal for different cartridges.
ENERGY is extremely important as long as the projectile holds together and penetrates.
 
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