Taylor KO Factor
Encyclopedia
Taylor KO Factor is a commonly used 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 figure of merit 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.
(Equation 1)
Where
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."
In Equation 1, the denominator value of 7000 is a scaling factor. It can be viewed one of two ways:
The TKOF has no physical meaning or scientific basis and is strictly used as a figure of merit for comparing cartridges. Its main advantage is the ability to attempt to represent complex terminal ballistics as a number. This can be utilized to assign different wounding capabilities to projectiles in video games.
The calculation is performed as shown in Equation 2.
(Equation 2)
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:
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 the it's 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:
500gr .458 Win Mag, 2150fps =70.33
500gr .500 S&W, 1200fps =42.86
450gr .45-70, 1250fps =36.48
440gr .500 Linebaugh, 1200fps= 37.71
370gr .475 Linebaugh, 1400fps =35.15
325gr .480 Ruger, 1350fps =29.77
300gr .375 H&H, 2550fps =40.98
300gr .405 Win, 2000fps =34.71
260gr .454 Casull, 1800fps =30.22
255gr .38-55, 1650fps =22.84
240gr .44 Mag, 1350fps =19.86
230gr .45 ACP, 830fps =12.30
200gr .35 Rem, 2100fps =21.06
170gr 30-06, 2850fps =20.76
165gr .40 S&W, 1080fps =10.44
158gr .357 Mag, 1400fps =11.28
150gr .30-30, 2250fps =14.85
115gr 9mm, 1250fps =7.31
85gr .243, 2950fps =8.70
71gr .32acp, 900fps =2.83
55gr .223, 3300fps =5.78
50gr .25acp, 750fps =1.33
30gr .22LR, 1400fps =1.33
Stopping power
Stopping power is a colloquial term used to describe the ability of a firearm or other weapon to cause a penetrating ballistic injury to a target, human or animal, sufficient to incapacitate the target where it stands....
of hunting cartridges. The term "KO" is an acronym for "Knock Out." The Taylor KO Factor (TKOF) is a figure of merit that allows hunters to compare bullets with respect to stopping power
Stopping power
Stopping power is a colloquial term used to describe the ability of a firearm or other weapon to cause a penetrating ballistic injury to a target, human or animal, sufficient to incapacitate the target where it stands....
. The TKOF was developed by John "Pondoro" Taylor, a famous mid-20th century hunter
Hunting
Hunting is the practice of pursuing any living thing, usually wildlife, for food, recreation, or trade. In present-day use, the term refers to lawful hunting, as distinguished from poaching, which is the killing, trapping or capture of the hunted species contrary to applicable law...
and poacher
Poaching
Poaching is the illegal taking of wild plants or animals contrary to local and international conservation and wildlife management laws. Violations of hunting laws and regulations are normally punishable by law and, collectively, such violations are known as poaching.It may be illegal and in...
of African big game. The factor is computed using Equation 1.
(Equation 1)Where
is the bullet mass in grains (1 poundPound (mass)The pound or pound-mass is a unit of mass used in the Imperial, United States customary and other systems of measurement...
= 7000 grainsGrain (measure)A grain is a unit of measurement of mass that is nominally based upon the mass of a single seed of a cereal. From the Bronze Age into the Renaissance the average masses of wheat and barley grains were part of the legal definition of units of mass. However, there is no evidence of any country ever...
)
is the bullet velocity in feet per secondFeet per secondThe foot per second is a unit of both speed and velocity . It expresses the distance in feet traveled or displaced, divided by the time in seconds...
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."
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 merit for comparing cartridges. Its main advantage is the ability to attempt to represent complex terminal ballistics as a number. This can be utilized to assign different wounding capabilities to projectiles in video games.
Example Calculation
Consider the case of a standard NATO 7.62 × 51 mm cartridge. It has the following characteristics:- diameter: 7.62 mm
0.30 inches - mass: 9.7 grams
150 grainGrain (measure)A grain is a unit of measurement of mass that is nominally based upon the mass of a single seed of a cereal. From the Bronze Age into the Renaissance the average masses of wheat and barley grains were part of the legal definition of units of mass. However, there is no evidence of any country ever...
bullet - velocity: 860 meters per second
2820 feet per secondFeet per secondThe foot per second is a unit of both speed and velocity . It expresses the distance in feet traveled or displaced, divided by the time in seconds...
The calculation is performed as shown in Equation 2.
(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 energyKinetic energyThe kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
- momentumMomentumIn classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
- 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 the it's 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:
500gr .458 Win Mag, 2150fps =70.33
500gr .500 S&W, 1200fps =42.86
450gr .45-70, 1250fps =36.48
440gr .500 Linebaugh, 1200fps= 37.71
370gr .475 Linebaugh, 1400fps =35.15
325gr .480 Ruger, 1350fps =29.77
300gr .375 H&H, 2550fps =40.98
300gr .405 Win, 2000fps =34.71
260gr .454 Casull, 1800fps =30.22
255gr .38-55, 1650fps =22.84
240gr .44 Mag, 1350fps =19.86
230gr .45 ACP, 830fps =12.30
200gr .35 Rem, 2100fps =21.06
170gr 30-06, 2850fps =20.76
165gr .40 S&W, 1080fps =10.44
158gr .357 Mag, 1400fps =11.28
150gr .30-30, 2250fps =14.85
115gr 9mm, 1250fps =7.31
85gr .243, 2950fps =8.70
71gr .32acp, 900fps =2.83
55gr .223, 3300fps =5.78
50gr .25acp, 750fps =1.33
30gr .22LR, 1400fps =1.33
See also
- Stopping powerStopping powerStopping power is a colloquial term used to describe the ability of a firearm or other weapon to cause a penetrating ballistic injury to a target, human or animal, sufficient to incapacitate the target where it stands....
- Taylor Knock-Out Factor Calculator
- Thorniley Stopping Power Calculator