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:

where:
m_bullet = Mass of the bullet in grains
v_bullet = velocity of the bullet in feet per second
d_bullet = 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 Factor	Name	Mass (gr)	Velocity (fps)	Bullet Diameter (in)
19.6	.308 Winchester	168	2650	0.308
147	.50 BMG	660	3050	0.510
4.72	.380 ACP	95	980	0.355
6.20	.38 Special	158	770	0.357
8.56	.357 Sig	125	1350	0.355
24.9	.300 Winchester Magnum	180	3146	0.308
4.64	5.45x39mm	49	3000	0.221
35.5	.338 Lapua Magnum	250	2940	0.338
20.8	7.62×54mmR	181	2580	0.312
70.3	.458 Winchester Magnum	500	2150	0.458
29.8	.480 Ruger	325	1350	0.475
19.9	.44 Magnum	240	1350	0.429
12.3	.45 ACP	230	830	0.452
20.8	.30-06 Springfield	170	2850	0.308
10.4	.40 S&W	165	1080	0.400
11.3	.357 Magnum	158	1400	0.357
14.9	.30-30 Winchester	150	2250	0.308
7.31	9mm Parabellum	115	1250	0.355
6.12	5.56 x 45 NATO	62	3100	0.224
1.33	.25 ACP	50	750	0.251
1.33	.22LR	30	1400	0.222

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.