This article was originally posted on another blog of mine in early 2012, but its content is more appropriate here, I think.
The Taylor Knock-Out Index may be the single worst metric available for determining the effectiveness of small arms ammunition. Despite this, it sees relatively widespread use, usually to compare two calibers that are obviously in different potency classes.
Why does the TKOI suck so bad?
Well, let's do an experiment: What is the Taylor Knock Out Factor of the Lambert Glacier?
Of course, if you stand in front of the glacier, you'll hardly get vaporized. Glaciers, unless you're on poorly navigated, fast-moving ships, are largely harmless.
And yet...
The TKOF equation goes something like this:
TKOF = (Mass x Velocity x Caliber)/7000
Units in the normal Imperial grains, feet/sec, and inches, of course.
So what's the TKO of the Lambert Glacier?
Well, the Lambert Glacier is about 100km wide, 400km long, and 2.5km deep.
To get volume, simply multiply:
100,000 x 400,000 x 2,500
= 100,000,000,000,000, or 100 trillion cubic meters volume.
The density of ice is 916,700 g/m^3
The mass of the Lambert Glacier is estimated to be approximately:
91,670,000,000,000,000,000, or 91.67 sextillion grams mass.
To find mass in grains, we simply multiply that by 15.43:
91.67 x 15.43 x 1 sextillion
=1,414,468,100,000,000,000,000, or 1.41 septillion grains mass.
What is the caliber of the Lambert Glacier? We'll go ahead and take its width and height, and average them:
(100,000m + 2,500m)/2
= 51,250m
Multiply by 3.28 and 12 to convert to inches:
=2,017,200, or 2.02 million inches.
What is the velocity of the Lambert Glacier?
It varies, but one source quotes 400 to 800m/year Let's do some quick math:
(400 + 800)/2
= 600 m/yr
600 m/yr x (1/(60x60x24x365)) yr/s
= .000019 m/s
.000019 m/s x 3.28 ft/m
= .0000624, or 62.4 microfeet per second
Now we can plug it all in!
TKOF = (Mass x Velocity x Caliber)/7000
TKOF = (1,414,468,100,000,000,000,000 x .0000624 x 2,017,200)/7000
Before we solve this equation, we need some reference. For comparison, a 7.62x51mm rifle round has a TKOF of 17.787, and a .45 ACP pistol round has a TKOF of 12.568.
Now, the Taylor Knock Out Factor of the Lambert Glacier is...
Wait for it...
Wait for it...
25,434,829,886,052,571,429 TKOF! That's over twenty five sextillion on the TKOI! The Lambert Glacier should have destroyed the Earth by now!
Quake in fear at the might of the Lambert Glacier, Destroyer of Worlds!
You retain too many sig figs in your straw man argument. Three is the max that you can jave based on your calculations above. In addition, grains don't interconvert between metric and imperial reliability, so your conversion factors are also off. Just because the glacier has more of the said factor, doesn't make the comparative values moot.
ReplyDelete"grains don't interconvert between metric and imperial reliability"
DeleteI'm sorry, what?
The TKO is useless as a predictive tool, and people try to apply it to things it was never meant to do, which was comparing hypothetical effectiveness of heavy medium and large bore safari rifles. You know those very expensive double and bolt rifles made only for hunting large, thick skinned, dangerous game using solid projectile bullets.
ReplyDeleteIn terms of being a comparative tool, it is fine when talking about that narrow range of safari rifles in terms of ballistics (much like muzzle energy is also a meaningless number for anything but comparison between two cartridges). It is not, and simply cannot be, a predictive tool for actual performance as the "reducto ad absurdum" with the glacier points out. The presumed target of the TKO is a sum total of Elephant, Rhino, Cape Buff, and Hippo, as all other dangerous or big game animals could easily be taken by a 303 Brit.
When you are talking such a narrow range of performance using solid bullets where the legal minimum is defined by the 375 H&H (or 9.3x62 in Zimbabwe) and the maximum is whatever your shoulder and wallet can stand there really isn't much to say but "bigger and heavier" is generally better (which is all the TKO ends up doing). But suffice to say, if you can't kill it with a 375 H&H, going to a bigger caliber isn't going to help you so the TKO of a 460 Weatherby isn't going to be the deciding factor in success or failure. Shot placement, shot placement, shot placement.