Wednesday, December 19, 2012

Measuring Effectiveness of Cartridges: Taylor KO Factor

In the previous two posts, we saw how some people obtain a figure of merit for a cartridge by measuring the kinetic energy and the momentum. While these two methods have a basis in physics, the next method which we will study in this post is more of an empirical formula. This is called the Taylor KO Factor (where the KO stands for Knock Out). This term is also sometimes called the Taylor Knock Out Formula or simply abbreviated as TKOF.

The inventor of this formula was a famous 20th century big-game hunter and ivory poacher named John Howard "Pondoro" Taylor. Born in Dublin, Ireland, he developed a passion for hunting and decided to become a professional hunter in Africa. As a result of this, he became an expert in hunting with various rifles and cartridge combinations. In a career spanning over thirty years, he is credited with hunting over 1,000 elephants (though many of these were illegally hunted) as well as thousands of other African big game like hippo, rhinos, lions, cape buffalo etc. He received the nickname "Pondoro" (meaning "lion" in some African languages) from some of the locals, because of his lion hunting skills. Allegedly he was so busy hunting in remote African jungles that he didn't realize that World War II had broken out (he signed up for the King's African Rifles regiment after he finally got the news!)

John "Pondoro" Taylor (1904-1969)

John Taylor wrote quite a few books on the subjects of big game hunting and African hunting. In one of his books, African Rifles and Cartridges, published in 1948, he makes mention of a formula he came up with to test for cartridge effectiveness when hunting big game.

The story behind his formula is that during his long hunting career, Taylor had observed that some cartridges were more suitable for stopping elephants than others. While he admitted that many cartridge types would work at killing an elephant when aimed accurately at an elephant's brain, he was more concerned with situations where he missed the brain and the elephant would become enraged and charge at him. He wanted to evaluate cartridges that could stun an elephant, even if the bullet didn't hit a lethal spot, reasoning that a "knock-out" blow on the elephant would give the hunter enough time to reload and follow up with a more accurately aimed shot. It was really meant to calculate the effectiveness of solid big-bore bullets. John Taylor himself used this formula to make the point that big-bore bullets were more effective at stopping larger game than the lighter and faster bullets available at that time.

His formula is an empirical one and is defined as:

mbullet = Mass of the bullet in grains
vbullet = velocity of the bullet in feet per second
dbullet = diameter of the bullet in inches.
The dividing by 7000 is because his formula converts grains to pounds (1 pound = 7000 grains).

The TKOF obtained by this equation is a dimensionless number, as there isn't really a science behind it and it is merely a figure of merit for comparing different cartridge types. A higher TKOF value indicates better stopping power for the cartridge. For people who like to work with metric units, the calculation is defined as:
TKOF = m * v * d / 3500

where m is in grams, v is in meters per second and d is in millimeters.

Consider a NATO standard 5.56x45 mm. cartridge. The bullet from this cartridge normally weighs 4 grams (62 grains), has a velocity of 940 meters/sec (3100 feet/sec) and a diameter of 5.70 mm. (.223 inches). Using these values in the above formula, we get TKOF = 6.12 approximately.

The following table lists TKOF values for some common cartridges:
(Figures taken from wikipedia)
TKO FactorNameMass (gr)Velocity (fps)Bullet Diameter (in)
19.6.308 Winchester16826500.308
147.50 BMG66030500.510
4.72.380 ACP959800.355
6.20.38 Special1587700.357
8.56.357 Sig12513500.355
24.9.300 Winchester Magnum18031460.308
35.5.338 Lapua Magnum25029400.338
70.3.458 Winchester Magnum50021500.458
29.8.480 Ruger32513500.475
19.9.44 Magnum24013500.429
12.3.45 ACP2308300.452
20.8.30-06 Springfield17028500.308
10.4.40 S&W16510800.400
11.3.357 Magnum15814000.357
14.9.30-30 Winchester15022500.308
7.319mm Parabellum11512500.355
6.125.56 x 45 NATO6231000.224
1.33.25 ACP507500.251

Per the above table, we can see that a .44 Magnum has better stopping power than a .45 ACP as it has a larger TKOF value, but a .308 Winchester is considered nearly equivalent to a .44 Magnum in stopping power since their TKOF values are close to each other. Similarly, it suggests that a 7.62x54mmR is equivalent to a .30-06 Springfield and .25 ACP is equivalent to .22LR in stopping power, while a .50 BMG outdistances everything else by a very wide margin.

Unlike the kinetic energy and momentum formulae, the Taylor KO Factor takes the bullet diameter into account as part of the calculation. It tends to favor big-bore heavy solid bullets and is really meant for big-game hunting. If we were to calculate the kinetic energy and momentum of 7.62x54mmR and .30-06 Springfield, they would both suggest different stopping powers for the cartridges, but per the Taylor KO Factor calculation, these two are pretty close to each other in stopping power.


  1. I've enjoyed your articles a lot. Thanks for all the interesting and useful information about guns!

  2. Taylor KO is Total Stupidity

    [from Wikipedia talk section] Consider, an Olympic shot put weighs 16 lbs., is about 4.8 inches in diameter, is made of steel, and leaves a world class throw with about 15.9 meters per second initial velocity. After conversions this is a TKO in excess of 3500. Note there is no engineering unit for this dim bulb formula because it means nothing. The shot has an initial kinetic energy of about 915 Joules, about the muzzle energy of a 125 grain .357 magnum.

    An elephant rifle chambered for the caliber .458 Lott cartridge launches a jacketed 500 grain lead bullet at about 2300 feet per second. This is a TKO of 75. The initial kinetic energy is about 7980 Joules.

    Which do you suppose will drop a charging bull elephant more effectively: an Olympic shot putter or a guy with an elephant rifle? John Taylor's formula says its the shot putter by a factor of over 40 times.

    Please stop propagating this foolishness, it has gone on long enough.

  3. This is a terrible comparison. If an olympic shot put has 16 lbs. of black powder, as intended by the formula, it would be a small bomb and would easily stop an elephant.