Taylor knock-out factor

The Taylor knock-out factor, also called Taylor KO factor or TKOF, is a formulaic mathematical approach for evaluating the stopping power of hunting cartridges, developed by John "Pondoro" Taylor in the middle of the 20th century. Taylor, an elephant hunter and author who wrote two books about rifles and cartridges for African hunting, devised the formula as a means of comparing the ability of a cartridge to deliver a knock out blow to an elephant from a shot to the head when the brain is missed.

Formula

The Taylor KO factor multiplies bullet mass (measured in grains) by muzzle velocity (measured in feet per second) by bullet diameter (measured in inches) and then divides the product by 7,000, converting the value from grains to pounds and giving a numerical value from 0 to ~150 for normal hunting cartridges. It is proportional to the momentum at the muzzle times the diameter of the bullet. Expressed as a fraction, the Taylor KO Factor is:^[1]^[2]^[3]^[4]

\mathrm {TKOF} ={\frac {Mass\times Velocity\times Diameter}{7000}}

Example calculation

Using the standard 7.62×51mm NATO cartridge, the cartridge's characteristics are:

Bullet mass = 9.5 grams $\Rightarrow$ 147 grains
Muzzle velocity = 833 meters per second $\Rightarrow$ 2733 feet per second
Bullet diameter = 7.82 millimetres $\Rightarrow$ .308 inches

The calculation is:

\mathrm {TKOF} ={\frac {147\times 2733\times .308}{7000}}=\mathrm {17.7}

Therefore the Taylor KO factor for the 7.62×51mm NATO cartridge is 17.7.

For metric values the calculation is

$\mathrm {TKOF} ={\frac {Mass\times Velocity\times Diameter}{3505,55}}$

7.62×51mm NATO in metric :

\mathrm {TKOF} ={\frac {9.5\times 833\times 7.82}{3505.55}}=\mathrm {17.7}

(note that 7.62 mm is the land diameter of the caliber, however the actual bullet diam is 7.82 mm)

Note: The product of mass and velocity is a quantity called, in modern physics, "momentum". Conservation of momentum is a characteristic of non-deformable collisions. A bullet, hitting hard bone, would transfer most of the impulse to that bone mass.

History

John "Pondoro" Taylor, an ivory hunter who over his career shot over 1,000 elephants along with a variety of other African game and who is renowned for writing two books about rifles and cartridges for African hunting, devised the Taylor KO factor to place a mathematical value on the concussive effects a cartridge and bullet would have on an elephant, specifically from a shot to the head when the brain is missed, a "knock out" meaning the elephant was sufficiently stunned by the hit that it would not immediately turn on the hunter or flee.^[2]^[4]^[5]^[6]^[7]^[8]

First describing the Taylor KO Factor as "knock out value" or "strike energy" in his African rifles and cartridges, Taylor wrote that muzzle energy is "surely the most misleading thing in the world", that it is too dependent on muzzle velocity instead of bullet weight and that it is "quite useless if you are trying to compare any two rifles from the point of view of the actual punch inflicted by the bullet" which according to him is more affected by the bullet's weight. In African rifles and cartridges Taylor compares the effect of a near miss of an elephant's brain from a frontal head shot with the .416 Rigby and the .470 Nitro Express, two cartridges with similar muzzle energy but different bullet weights. Taylor states that the .416 Rigby will probably not knock the elephant out, but momentarily stun the animal which will recover quickly if not dispatched immediately, while the same shot delivered by the .470 Nitro Express will render the elephant unconscious for up to five minutes. Further, Taylor writes that the .577 Nitro Express will knock an elephant unconscious for around 20 minutes, the .600 Nitro Express around half an hour.^[4]^[6]

The Taylor KO factor conforms to the observations and experiences of Taylor who, along with other very successful elephant hunters such as Deaf Banks, Pete Pearson and Jim Sutherland, preferred large heavy bore rifles for elephant hunting in close country.^[2]^[4]^[9]

Criticism

Whilst most acknowledge the originality of the formula and Taylor's broad big-game hunting experience with a wide variety of cartridges, the Taylor KO factor is source of some debate amongst modern gun writers, some describing it as peculiar, antiquated, inaccurate and an unfounded theory, others stating it is a useful tool but stressing that should not be used in isolation when choosing a big-game hunting cartridge, whilst others still say their experiences tend to support the formula.^[1]^[2]^[10]^[11]^[12]

Specific criticisms of the Taylor KO Factor include the emphasis placed on bullet diameter over factors such as sectional density and bullet expansion and the formula’s failure to account for modern bullet design. These factors, along with Taylor’s dismissal of muzzle energy, allow many obsolete low powered large bore cartridges such as the .577/450 Martini-Henry and the .45-70 Government to have as much as twice the TKOF than the smaller bore general purpose hunting cartridges such as the .303 British and the .30-06 Springfield. For these reasons the Taylor KO factor is seen as poor measure of stopping power for cartridges used on deer sized game and smaller, it is also seen as a poor measure of the performance of handgun cartridges.^[1]^[2]^[3]^[13]

Taylor himself acknowledged this, stating "in the case of soft-skinned non-dangerous game, such as is generally shot at medium to long ranges, theoretical mathematical energy may possibly prove a more reliable guide" and that his formula was designed to measure a cartridge's performance against the large, thick skinned, big boned elephant.^[4]

TKOF comparison

Below is a table including a number of African dangerous game hunting cartridges including their bullet mass, muzzle velocity, bullet diameter and Taylor KO factor, discussed in African rifles and cartridges.^[4]

TKOF	Name	Mass		Velocity		Diameter
TKOF	Name	gr	g	ft/s	m/s	in	mm
1.5	.22 Long Rifle †	40	2.6	1,200	370	.223	5.7
5.6	5.56×45mm NATO † ‡	62	4.0	2,830	860	.224	5.7
16.0	.277 Fury † ‡	135	8.7	3,000	910	.278	7.1
17.9	7.62×51mm NATO † ‡	147	9.5	2,733	833	.308	7.8
28.3	.318 Westley Richards	250	16.2	2,400	730	.330	8.4
31.4	.333 Jeffery	300	19.4	2,200	670	.333	8.5
30.4	.338 Winchester Magnum ‡	225	14.6	2,800	850	.338	8.6
30.2	.350 Rigby	225	14.6	2,625	800	.358	9.1
34.6	.375 H&H Magnum	235	15.2	2,750	840	.375	9.5
35.3	9.3×62mm Mauser	286	18.5	2,362	720	.366	9.3
38.8	.375 H&H Magnum	300	19.4	2,400	730	.375	9.5
49.2	.400 Jeffery Nitro Express	400	25.9	2,100	640	.410	10.4
49.8	.450/400 Nitro Express	400	25.9	2,150	660	.405	10.3
51.4	.404 Jeffery	400	25.9	2,125	648	.423	10.7
57.1	.416 Rigby	400	25.9	2,400	730	.416	10.6
59.9	.425 Westley Richards	410	26.6	2,350	720	.435	11.0
67.5	.450 Nitro Express	480	31.1	2,150	660	.458	11.6
69.3	.450 No 2 Nitro Express	480	31.1	2,175	663	.458	11.6
74.7	.450 Rigby ‡	480	31.1	2,378	725	.458	11.6
70.3	.458 Winchester Magnum ‡	500	32.4	2,150	660	.458	11.6
76.2	.465 H&H Magnum ‡	480	31.1	2,375	724	.468	11.9
69.0	.500/465 Nitro Express	480	31.1	2,150	660	.468	11.9
72.9	.470 Nitro Express	500	32.4	2,150	660	.475	12.1
89.3	.500 Nitro Express	570	36.9	2,150	660	.510	13.0
90.9	.505 Gibbs	600	38.9	2,100	640	.505	12.8
128.3	.577 Nitro Express	750	48.6	2,050	620	.584	14.8
147.5	.600 Nitro Express	900	58.3	1,850	560	.620	15.7
200.0	.700 Nitro Express ‡	1,000	64.8	2,000	610	.700	17.8

† Included as a comparison
‡ Developed after Taylor's writings

References

^ ^a ^b ^c Steven Bowers, "The best all-round large bore rifle cartridge", African Expedition Magazine, vol 1 issue 2, Safari Media Africa, September 2008.
^ ^a ^b ^c ^d ^e Chuck Hawks, "The Taylor Knock-Out Factor", chuckhawks.com, retrieved 10 April 2018.
^ ^a ^b Philip P. Massaro, Big book of ballistics, Gun Digest Books, Iola, 2017, ISBN 978-1-4402-4711-8.
^ ^a ^b ^c ^d ^e ^f John Taylor, African rifles and cartridges, Gun Room, London, 1948.
^ Jim Carmichel, "Knockdown power: Here's why some calibers always seem to flatten game", outdoorlife.com, retrieved 1 June 2018.
^ ^a ^b John Taylor, Big game and big game rifles, Herbert Jenkins, London, 1948.
^ Brad Fitzpatrick, "Knockout punch", RifleShooter Magazine’s guide to big-game hunting, Skyhorse Publishing, New York, 2017, ISBN 978-1-5107-2076-3.
^ Terry Weiland, Dangerous game rifles, 2nd ed, A Shooting Sportsman Book, 2009, ISBN 978-0-89272-807-7.
^ James H. Sutherland, The adventures of an elephant hunter, Macmillan, London, 1912.
^ Finn Aagaard, "Stopping power", huntforever.org, retrieved 4 June 2018.
^ John McAdams, "Pros and cons of using the Taylor Knock-Out Factor", exclusive.multibriefs.com, retrieved 5 May 2018.
^ Randy Wakeman, "Energy transfer and other bullet bullistics", randywakeman.com, retrieved 5 June 2018.
^ Patrick Sweeny, Choosing handgun ammo: the facts that matter most for self-defense, Gun Digest Books, Zephyr Cove NV, 2017, ISBN 978-1-946267-03-0.

External links

N4LCD, "Energy, momentum and Taylor KO calculator", n4lcd.com, retrieved 4 June 2018.

[Bowers-1] Steven Bowers, "The best all-round large bore rifle cartridge", African Expedition Magazine, vol 1 issue 2, Safari Media Africa, September 2008.

[Hawks-2] Chuck Hawks, "The Taylor Knock-Out Factor", chuckhawks.com, retrieved 10 April 2018.

[Massaro-3] Philip P. Massaro, Big book of ballistics, Gun Digest Books, Iola, 2017, ISBN 978-1-4402-4711-8.

[Taylor-rifles-cartridges-4] ^ ^a ^b ^c ^d ^e ^f John Taylor, African rifles and cartridges, Gun Room, London, 1948.

[Carmichel-5] Jim Carmichel, "Knockdown power: Here's why some calibers always seem to flatten game", outdoorlife.com, retrieved 1 June 2018.

[Taylor-big-game-6] John Taylor, Big game and big game rifles, Herbert Jenkins, London, 1948.

[Fitzpatrick-7] Brad Fitzpatrick, "Knockout punch", RifleShooter Magazine’s guide to big-game hunting, Skyhorse Publishing, New York, 2017, ISBN 978-1-5107-2076-3.

[Weiland-8] Terry Weiland, Dangerous game rifles, 2nd ed, A Shooting Sportsman Book, 2009, ISBN 978-0-89272-807-7.

[Sutherland-9] James H. Sutherland, The adventures of an elephant hunter, Macmillan, London, 1912.

[AAgaard-10] Finn Aagaard, "Stopping power", huntforever.org, retrieved 4 June 2018.

[McAdams-11] John McAdams, "Pros and cons of using the Taylor Knock-Out Factor", exclusive.multibriefs.com, retrieved 5 May 2018.

[Wakeman-12] Randy Wakeman, "Energy transfer and other bullet bullistics", randywakeman.com, retrieved 5 June 2018.

[Sweeny-13] Patrick Sweeny, Choosing handgun ammo: the facts that matter most for self-defense, Gun Digest Books, Zephyr Cove NV, 2017, ISBN 978-1-946267-03-0.

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