Re: 416 Opinions Required
Taylor Knockdown Formula
Great White Hunter John "Pondoro" Taylor suggested the Taylor Knockdown formula (TKO), sometimes called "Taylor Index", which integrates calibre and momentum to generate a relative value that is a guide to the potential of a round to incapacite a target.
TKO value = [ Weight (gr) x Terminal Velocity (fps) x calibre (in) ] ÷ 7000
This obviously does not take into account any factors such a bullet shape, construction, design or tendency to tumble, mushroom or fragment. In this respect the basic TKO offers a indication of the minimal performance one could expect from a round. It is, however, still a useful tool for comparing loads and gaining some idea how a round may perform if it fails to mushroom. I don't think the TKO is exact enough to let you say that, for example, a round with a TKO of 15 has twice the likelihood of stopping someone as a round with a TKO of 7, but a load with a higher TKO will usually be a better choice for defensive applications.
Taylor Index and suggested levels for hunting
Most pistol hollowpoint rounds are designed to expand to 150% of their original diameter, so one can multiply the calibre by 1.5 to get an idea of how the round will perform if it mushrooms. Since we don't know the likelihood of mushrooming we must express the bullet's TKO value as a range rather than an average. Therefore a 230gr Hollowpoint .45 at 850fps has a TKO of 12.57-18.85 and a 124gr 9mm Hollowpoint at 1200fps has a TKO of 7.55-11.32.
Some argue that TKO is only useful for comparing pistol bullets to pistol bullets or rifle to rifle. Some hunters that have used both handguns and rifles assert that TKO is relevant for comparison. A 44 magnum 240gr at 1400fps with a TKO=20.6 is more likely to drop a deer more often than a .270 Win 130gr at 3100fps with a TKO=15.9.
John Linebaugh on TKO
If there is a discrepancy, it is in comparing bullets with a high tendency to tumble with those that do not. One factor I don't think TKO figures in is the tumbling of modern spitzer bullets. I suspect that many of the hunting weapons Taylor used used round nose ammo –this would certainly be true of the large calibre big game weapons.
If a bullet tumbles then at some time during its rotation it will present its lateral areas, which will be larger than its frontal area. Suppose we multiply a bullet's length by its calibre, and use a correction factor of, say, 0.75 to allow for the shape not being a rectangle. This gives us an approximate area for the side of bullet. If we divide that area by &#960; , take the square root and multiply by 2 then we have the equivalent bullet diameter that would have the same area. For a 62gr 5.56mm round of 0.224 x 0.906 area is equivalent to a 0.44 bullet, and for a 150gr 7.62mm bullet of 0.30 x 1.28 area is equivalent to 0.60 calibre. As a "Quick and Dirty" calculation we can simply double the calibre.
TKO of a 5.56mm 62gr at 3100fps will therefore range from 6.15-12.08 and for a 7.62mm NATO 150gr at 2750fps as 17.68-35.36.
This would seem to agree with the observation that the 5.56mm often displays very variable stopping power. For the 5.56mm I think the true TKO is in fact much higher, since the round causes extra damage if it fragments. I've not idea how to quantify this, however.
As I've stated earlier, comparison of a bullet's momentum is only really relevant when calibers are similar, and the TKO illustrates this. If two rounds have the same TKO, then by definition they will have the similar performance when it comes to incapacitating a target. The smaller calibre round would have a higher momentum to give it the same final TKO. A .45 with a TKO of 12.57 has a momentum of 28ftlb/sec. A 180gr .357 at 1369fps has the same TKO and a momentum of 35.2ftlb/sec. The smaller, higher momentum round should move an object it hits at a higher speed than the larger, but the TKO is the same, illustrating the effect the larger calibre has. A higher momentum is therefore only an indication of a better round if the round is of the same or larger calibre.
The Taylor Index - A Measure of Stopping Power
We sometimes get a question such as "How do I compare the effectiveness, of one cartridge, say a .450 Marlin over a 30-06? I want to purchase a deer/bear rifle for woods and need some guidance."
Hunters and shooters have been searching a long time for the magic formula that will predict what is needed to drop an animal in his tracks, every time. No such formula has been developed, but this doesn't keep people from trying. Many thought that the kinetic energy of the bullet was a reasonable measure of the stopping power of the bullet and most bullet and ammunition manufacturers catalogs provide charts that show the velocity and kinetic energy of a given bullet anywhere along its trajectory.
The equation for this energy calculation is:
KE = m*v2/2 = bw*v2/450436 (1)
KE = Kinetic Energy, ft-lbs
m = bullet mass, slugs
v = bullet velocity, f.p.s.
bw = Bullet weight, grs.
Noted big game hunter and writer John Taylor thought that the kinetic energy equation gave too much credit to the new high velocity cartridges. Taylor, who spent a good many years in Mozambique, did a great deal of shooting and some commercial ivory hunting. He wrote a book entitled African rifles and Cartridges in which he pushed the British big-bore viewpoint. He thought these new cartridges, which fired a lightweight bullet at high velocity, gave too much importance to bullet velocity. Looking at the kinetic energy equation it can be seen that a small increase in velocity means a large increase in the kinetic energy because this energy increases as the square of the velocity. He thought that this would lead the hunter to believe that a small bullet, at high velocity, would be more effective on big game than a slower, heavier bullet. He stated that based on his hunting experience this was not so.
In an article in the November, 1947 issue of the American Rifleman magazine, Taylor gave several examples of how the heavier bullet knocked big game animals cold while the lighter faster bullet, in many cases, only dazed the animal for a few seconds. Taylor's energy equation is listed below:
TI = bw/7000*v*DI (2)
TI = Taylor Index
bw = Bullet weight, grs
v = bullet velocity, f.p.s.
DI = Bullet diameter, inches
Taylor's equation includes the bullet diameter, velocity and bullet weight. Since the velocity term is not squared it has less impact on TI energy as compared to the kinetic energy equation.
Table 1.0 shown below lists several popular cartridges and the generated kinetic energy (K.E.) and Taylor Index (TI).
(grains) Muzzle Vel.
(f.p.s.) 100 yd. Vel.
(f.p.s.) 100 yd. K.E.
(ft.-lb.) 100 yd.
22 Long Rifle 40 1150 976 85 1.2
223 Rem. 53 3330 2865 966 4.9
7mm Rem. Mag. 154 3200 2966 3008 18.5
308 Win. 150 2820 2593 2239 17.1
30-06 180 2700 2484 2466 19.7
416 Rigby 400 2400 2184 4236 51.9
450 Marlin 350 2100 1710 2272 39.2
470 N.E. 500 2150 1907 4037 64.6
50 BMG 750 2769 2681 11965 146.5
Note: All velocities and energies shown were calculated using the LFDW program.
From Table 1.0 it can be seen that the 450 Marlin develops only about 92% of the 30-06's kinetic energy at 100 yd, but the Taylor Index for the 450 Marlin is almost double that of the 30-06. Based on this information and the fact that heavier bullets usually work better in brush, the 450 Marlin looks like a winner. The last cartridge listed, the 50 BMG, is not considered a sporting cartridge, but was included to show how much energy this military cartridge can develop in comparison to other cartridges.
The Taylor Index is a relative value, which means the value has no units of measurement like ft.-lbs. or feet per second. It is more of an indicator of how one cartridge stacks up against another. This assumes, in all cases, that a well placed shot will be delivered to the vital area using a properly constructed bullet that will transfer all its energy to the game animal.
So, you might ask, "How do I use this information?" What we need is a chart of the Taylor Index figures rated against different type/size game. Listed below is my evaluation of such a table. Your ideas may differ and that's fine, but it is a starting place.
1-3 Crows, Squirrels, rabbits and skunks
3-5 Prairie dogs, ground hogs and coyotes
6-17 Antelope, mule deer and sheep - Open country
17-20 White tail deer, black bear - Brush/Woods
20-40 Elk, moose, Grizzly bear
40-50 Lion and other thin skinned dangerous game
50-125 Rhino, elephant or other thick skinned dangerous game
125-200 Any animal that roams the earth