Diagonal functor

Taylor KO Factor is a formulaic mathematical approach for evaluating the stopping power of hunting cartridges. The term "KO" is an acronym for "Knock Out." The Taylor KO Factor (TKOF) is a derived figure that allows hunters to compare bullets with respect to stopping power. The TKOF was developed by John "Pondoro" Taylor, a famous mid-20th century hunter and poacher of African big game. The factor is computed using Equation 1.

T K O F = \frac{m_{b u l l e t} \cdot v_{b u l l e t} \cdot d_{b u l l e t}}{7000}

(Equation 1)

Where

$m_{B u l l e t}$ is the bullet mass in grains (1 pound = 7000 grains)
$v_{B u l l e t}$ is the bullet velocity in feet per second
$d_{B u l l e t}$ is the bullet diameter in inches

If the international standard units of grams, millimeters, and meters per second are substituted, the divisor can be changed from 7000 to 3500 to give approximately the same resulting TKOF.

Taylor first described this measure of stopping power in his classic work "African Rifles and Cartridges" (Reference 1). In this work, Taylor did not actually state Equation 1. In fact, he stated in Reference 1 that "I do not think there is any necessity to go into the methods I employed to arrive at the formula I used, suffice it to say that the final figures agree in an altogether remarkable way with the actual performance of the rifles under practical hunting conditions." However, it is obvious from the text and his presentation that he used Equation 1.

Taylor referred to number generated by Equation 1 as the "Knock Out Value" or "Strike Energy." Common practice today is to refer to this value as the "Taylor KO factor" or simply "Taylor KO."Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

In Equation 1, the denominator value of 7000 is a scaling factor. It can be viewed one of two ways:

as converting the units of bullet mass from grains to pounds.
giving the TKOF a convenient numerical value from 0 to ~150 for normal hunting cartridges.

The TKOF has no physical meaning or scientific basis and is strictly used as a figure of meritPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. for comparing cartridges. Its main advantage is the ability to attempt to represent complex terminal ballistics as a number.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. This can be utilized to assign different wounding capabilities to projectiles in video games.Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park.

Background

Example Calculation

Consider the case of a standard NATO 7.62 × 51 mm cartridge. It has the following characteristics:

diameter: 7.62 mm $\Rightarrow$ 0.30 inches
mass: 9.7 grams $\Rightarrow$ 150 grain bullet
velocity: 860 meters per second $\Rightarrow$ 2820 feet per second

The calculation is performed as shown in Equation 2.

T K O F = \frac{0.30 \cdot 150 \cdot 2820}{7000} = 18.1

(Equation 2)

Alternative Approaches

Using numerical methods to evaluate the effectiveness of rifle cartridges has a long history and has been subject of much debate. The most common numerical methods used to evaluate the stopping power of cartridges are:

kinetic energy
momentum
TKOF
Thorniley Stopping Power

Each figure of merit weighs the cartridge characteristics differently. Some methods are based on fundamental physics (e.g. kinetic energy), while other methods are based on heuristic methods. Some of the more common figures of merit are:

kinetic energy: favors high velocity, lower mass bullets (no diameter dependence)
momentum: favors moderate velocity, moderate mass bullets (no diameter dependence)
TKOF: favors large diameter, moderate velocity, heavy bullets
Thorniley Stopping Power: favors moderate diameter, moderate velocity, moderate mass bullets

None of these methods truly consider bullet construction, with the exception of TKO, which dealt mainly with solid bullets. An expanding bullet, for example, may have better "stopping" power over another design, due to its increased wound channel as the jacket opens, even though it may be traveling at a lower velocity. Just as a large diameter solid, at low velocity may have better "stopping" power, due to its deep penetration, than a small diameter hollowpoint at max velocity.

Bullet shape does not factor in these methods either. Example: A solid, wide flat nosed bullet, may create more impact damage, than a solid, pointed or round nosed bullet of the same caliber at the same velocity.

These variables combine to effect bullet penetration, and tissue damage, in different ways. Thus making a simple, single method of bullet effectiveness, difficult to quantify.

Some examples of TKO factor's, and the factory loaded cartridge's derived from, are as follows:

TKO Factor	Name	Mass (gr)	Velocity (fps)	Bullet Diameter (in)
1074.9	.950 JDJ	3600	2200	0.950
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
13.3	7.62 Soviet	123	2420	0.312
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
42.9	.500 S&W Magnum	500	1200	0.500
36.5	.45-70	450	1250	0.458
37.7	.500 Linebaugh	440	1200	0.510
35.2	.475 Linebaugh	370	1400	0.475
29.8	.480 Ruger	325	1350	0.475
41.0	.375 H&H	300	2550	0.375
34.7	.405 Winchester	300	2000	0.4115
30.2	.454 Casull	260	1800	0.452
22.8	.38-55 Winchester	255	1650	0.3775
19.9	.44 Magnum	240	1350	0.429
12.3	.45 ACP	230	830	0.452
21.1	.35 Remington	200	2100	0.358
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
9.2	.327 Magnum	115	1800	0.312
14.9	.30-30 Winchester	150	2250	0.308
7.31	9mm Parabellum	115	1250	0.355
8.70	.243 Winchester	85	2950	0.240
2.83	.32 ACP	71	900	0.309
5.78	.223 Remington	55	3300	0.224
1.33	.25 ACP	50	750	0.251
1.33	.22LR	30	1400	0.222

References

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20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

My blog: http://www.primaboinca.com/view_profile.php?userid=5889534

Diagonal functor

Contents

Background

Example Calculation

Alternative Approaches

References

Further reading

See also

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Diagonal functor

Background

Example Calculation

Alternative Approaches

References

Further reading

See also

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