Thursday, April 9, 2015

The Taylor Knock-Out Index Is Useless

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!