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!

Saturday, February 21, 2015

All My TFB Posts On The M1 Garand

The M1 Garand has been the subject of much of my writing over at TFB, since it is a fascinating design, at once revolutionary and deeply flawed. Its descendant, the M14, is to this day a controversial weapon; at once the longest serving rifle and the shortest serving standard issue rifle in U.S. military history, it's a rifle that will virtually always deeply polarize a conversation with its mention.

I have decided to collect the posts I have so far done on the M1 Garand and the M14 rifle, for the convenience of my readership. They are, in chronological posting order, as follows:

Hindsight Is 30/06: A Critique Of The M1 Garand
Making The M1 Garand
The Great Rifle Controversy: 1955
Eight Reasons Selfloading Rifles Had To Wait For John Garand
Rifle Competition: US vs. UK in 1950 (DTIC)
InRange TV’s Heinous M1A Abuse
Small Caliber Book Reviews: U.S. Rifle M14, From John Garand To The M21
Two USMC Marksmanship Training Films Compared
The M1 Garand In The Dust And Mud, 1950

I will definitely be posting more about these rifles in the future; in particular, I have upcoming a post on the "light rifle" concept, as full-power automatic infantry rifles were once called, which I hope will prove to be a definitive design case study on that concept.

Friday, December 26, 2014

RPM Goes Mainstream

It's certainly true that I haven't posted an article here on 196,800 Revolutions Per Minute since May. Despite this, I am having more success blogging about small arms technology than I ever thought I would.

The few readers I have will already know that I am now full-time blogging at Instead of posting an article every month here, and accepting a modest check from Google, I am blogging full time at TFB, posting thirteen articles per week and covering both big and small topics. I have essentially complete creative control there; there is a considerable degree of separation between the people who pay the bills and those who do the writing. I won't pull the curtain back too much on TFB, but the content you see from me there is what you would get were I posting on my own time here (except I can post much, much more often at TFB, thanks to not having to work as much). When I first started working there, I was concerned that I would be forced to post on topics I did not care about, or that there would be a lot of micro-managing coming from the top. Not only did this not turn out to be the case, but thanks to the paycheck I get there I can buy more books (and I have more time to read them), meaning I am essentially working full time to bring my readers the best writing that I can, informed by both the additional resources at my disposal and by the extra opportunities being a writer there affords me. Indeed, so complete has my control over my content been as a writer for TFB that this blog has remained without update for so long; originally, I planned to continue posting here those articles I felt didn't fit in TFB, or would be too risque to ask the bosses to pay for. So far, it has been the case that no articles I have written proved unsuitable for TFB, and this blog has been all but abandoned as a result.

Steve asked me once if I enjoyed writing for TFB - he maintains that he wants his writers to enjoy their work. In truth, writing for them has been nothing short of magical for me. I am employed doing what I love (running my mouth - err, fingers), as a result of this I can write articles I never would have been able to without being paid, and I reach an audience that few other history-oriented bloggers do.

RPM will be updated again - if and when I find something appropriate that does not pass muster at TFB. In the meantime, I'd like to share a few articles I've written that I feel are among my best, as well as my contact information.

Before The Sturmgewehr: Assault Rifle Developments Prior to 1942
Energy: Don’t Sweat It!
A Short (Stroke) History of Tappet Operation, Part I: How It Works
Firearms Semantics: “Battle Rifle” and “Assault Rifle”
A Short (Stroke) History of Tappet Operation, Part II: Early Tappet Designs
How To Find Case Capacity With SolidWorks
A Short (Stroke) History of Tappet Operation, Part III: The M1 Carbine Cometh
The US Army Marksmanship Unit’s .264 USA
8 Uncommon Rifle Shooting Tips For Beginners
Ten 20th Century Military Rifles History Has Forgotten
Hindsight Is 30/06: A Critique Of The M1 Garand
Small Arms Technology: Has It Really Plateaued?

Contact info:
Twitter: @TFB_Nathaniel_F

Tuesday, May 13, 2014

Are U.S. Soldiers Dying From Inadequate Weapons? No.

I dislike doing rebuttal posts. The temptation is strong to adopt a simple quote-and-refute style, which costs little time and allows me to return to my only modestly interesting but very necessary daily life. This style is only compatible with lazy writing, however, and it's bad form to use it too often. Even so, there is a need for a direct response to some works of "journalism" which rely on sensationalist headlines over content to get attention, and which spread falsehoods, misconceptions, and sometimes even outright lies in the process.

I was asked by a friend what I thought about this hit piece on the M16/M4 platform and the 5.56mm caliber, which I decided offered me an opportunity to write a little more about the subject. As if anyone felt I hadn't already written enough, that is. Interestingly, the piece was written by Tom Kratman - a name I had to google - who is apparently a veteran of the 5th Special Forces Group and of 19 years in regular Army, eventually retiring at O-5 (the same as my father, of a different branch, coincidentally). He also writes science fiction for Baen, the same publisher where the old THR (a major haunt of mine, once upon a time) moderator Larry Correia now writes.

Kratman is then no neophyte as a writer or novice to military thinking, but this in my opinion only lends a hue of bafflement to his two EveryJoe articles. This man was special forces, and an officer, I must keep reminding myself as I read every tired myth, regurgitated piece of gunwriter hype, and mis-remembered factoid.

It is difficult for me to not be critical of the pieces, both from a factual and a writing standpoint. When my inner monologue reads the figures on my liquid crystal display, I am taken back to caffeine-and-pizza fueled spring mornings and afternoons, sitting in one piece chair-desks intended for the tiny Japanese furniture maker who designed them while listening to a youth who hasn't yet learned to shave the few wisps of a Van Dyke growing on his otherwise newborn face wring out a thin argument he decided on a week before. "Write something we can sell," I wonder if that phrase was ever uttered aloud or transmitted via electrons down copper wires during the planning phase of these two articles. Or perhaps Mr. Kratman truly believes in his premature ideas, which are so poorly supported they are in free-fall, about to reach terminal velocity.

"Remember, he was in 5th Special Forces Group, and a Lieutenant Colonel," again.

Let's step back. Many people disagree with me regarding my opinions of the AR-15 rifle family and the 5.56mm cartridge especially. Some of those people, I can hold a discourse with, and present the evidence I have for my position as best I can, to reach a mutual understanding of ideas, experiences, and views which led our opinions to where they are. Some I cannot, because they are too used to fighting the good fight; too zealous for a true mutual discourse.

Many more are too wrapped up in thin premises fed to them via casual reading of the latest issues of tactical magazines in the Barnes & Noble to really have a decent conversation with. It's this last kind that Mr. Kratman most closely resembles, from his escape-velocity exaggeration of the differences in capability of the M4 carbine and M16 rifle, to his mis-placed snark about the vagueness of the ACR program from the 1980s and 1990s. This last plays off an assumption that isn't true - that the ACR program demanded a deliberately vague "100% improvement" over the M16, begetting the almost laughably inane comment: "That means that we will never have a rifle that’s 99% better." In truth, the ACR program's goal was very specific: The winning rifle had to demonstrate a 100% improvement in hit probability during a highly sophisticated course designed specifically to measure that factor with soldiers under combat stress.

None of the rifles even came close. None of the advanced concepts, not burst fire, not caseless ammunition, not four power optical sights, improved the probability of a hit anywhere close to 100% over the M16A2 rifle. Those design elements that did significantly aid the hit probability - most notably optical sights - were incorporated into future AR-15 pattern service rifles and are in use today. To Mr. Kratman, however, the M4A1 with laser, CCO, vertical grip, and light might as well be an M16A2. The degree to which this is true is irrelevant - A G11 might as well be an M16A2 in terms of hit probability, something that Mr. Kratman ignores in favor of the white-noise-esque "they're failing our boys!" drone.

Kratman rounds out the article with more sophomoric whinging dressed as snark, and an off comment about the French. "A Lieutenant Colonel and veteran of the 5th SFG..." Yes, of course, I mustn't forget.

His follow up begins by repeating another half-truth about the M16; that the Army never wanted it and it was all McNamara's fault, a "fact" that ignores that the Army agreed to cancel M14 production in favor of the extremely ambitious SPIW, and McNamara was forcing them to, you know, actually provide rifles to the troops in the meantime. It may be presumptuous of me to think that this is something armies are expected to do, but I'll risk it. Eventually, SPIW crashed and burned, and the surprisingly good M16 became the mainstay of the Army for a half-century. None of this matters to Kratman, of course, since it doesn't make for good copy.

Where some sensationalist gunwriters would take a "back to basics" tack, and suggest re-adopting the M14 in .280 British or some such nonsense, Kratman instead talks about some potential technological improvements that could be in the pipeline for small arms, along with a number of other things that rifle salesmen want you to believe are technological improvements, but actually aren't. His list goes: 1. Intermediate-intermediate calibers, 2. Hyper burst, 3. Carbon-fiber barrels, 4. Electronic ignition, 5. Plastic cased ammunition, 6. Caseless ammunition, 7. A gas piston operating rod, and 8. Optical sights. 2, 3, 4, and 5 fit in with potential technologies that could improve the rifles of the future, 1 and 7 mostly sell rifles, not really offering anything over the 5.56mm cartridge and the AR-15 platform, 6 is all but dead due to technical issues, and 8 has already been implemented, further calcifying my suspicion that Mr. Kratman's technical knowledge of the subject is stuck in 1991.

What's strange is that he doesn't use this list to paint a rosy picture of the future of small arms in contrast to its oft-claimed stagnation; he uses it (in yet another attempt) to bash the M16. As if, somehow, they could have issued rifles then in 1964 that utilized technologies that are just now maturing to a basic level of feasibility. Some early AR series rifles did trial composite barrels and carbon-fiber handguards, features subsequently deleted in later versions because they didn't work very well then. It's as if Mr. Kratman doesn't understand that just having a working prototype doesn't mean you can make ten million rugged, mature, combat-ready weapons.

"A Lieutenant Colonel and veteran of the 5th SFG," I must remind myself.

It's bizarre to read a piece so sophomoric and poorly researched and constructed, only to follow the authorship trail and read a biography that impressive. Simply put, while I do not demand that everything I read reinforce my own opinions and ideas, I do not expect this sort of thing from a Special Forces Group veteran, much less one who's an O-5 rank and who gets paid to write for a living.

Sunday, April 20, 2014

On Combat Shooting (Part II)

Anthony G. Williams, in his article Assault Rifles And Their Ammunition: History and Prospects cites this line from Dual Path Strategy Series: Part III - Soldier Battlefield Effectiveness written by the PEO Soldier G5, Strategic Communications Office in August of 2011, to support his idea for a 6.5mm general purpose cartridge (GPC):
"Ultimately, Army service rifles must be general purpose in nature and embody a series of tradeoffs that balance optimum performance for a wide range of possible missions in a range of operating environments. With global missions taking Soldiers from islands to mountains and jungles to deserts, the Army can’t buy 1.1 million new service rifles every time it’s called upon to operate in a different environment."
However, earlier in that paper is contained this section on the range of the rifleman:
The maximum effective range of a weapon system is also a key element as it represents the potential for how far out a Soldier can effectively engage the enemy. This is also critical as it affects a Soldier’s ability to leverage an overmatch advantage. Doctrinally, this means that a Soldier will look to engage the enemy at a range that is greater than the range at which they can be engaged by enemy fire (typically 20 percent). According to FM 3-22.9, Rifle Marksmanship M16/M4 Series, there are three ranges of concern. First, there is the detection range, which must be well beyond the effective range of the weapon system. This provides the Soldier time to prepare to engage the enemy at the farthest possible ranges. The next band is the range overmatch distance, whereby friendly Soldiers can engage the enemy, but the enemy cannot engage the Soldiers. The final band is the threat engagement range where enemy personnel can target friendly forces.

Optimally, friendly forces will engage as the enemy enters the range overmatch area. This advantage is short lived however, since a quickly approaching enemy can move through this area in seconds. For example, according to The Encyclopedia of Land Warfare in the 20th Century, the effective range for AK-47 fired on semi automatic is 400 meters. The effective range for an M4 Carbine is 500 meters. The 100 meter difference provides a decisive range overmatch capability so long as Soldiers are proficient at hitting targets at the 400-500 meter range, which is why extensive marksmanship training is so critical.

The range of a weapon system relies heavily on the ammunition the weapon fires and the length of the barrel. Systems that utilize 5.56mm ammunition typically cite ranges of 500 – 550 meters for point targets while U.S. weapon systems that fire 7.62x51mm typically cite ranges closer to 800 meters for point targets. The rounds actually travel further but tend to destabilize after they slow to subsonic speeds and therefore lose accuracy. Longer barrels allow more of the propellant's energy to be transferred to the projectile, resulting in greater range. The spiral grooves inside a rifled barrel impart spin to the round. The spin stabilizes the round which provides accuracy, though it doesn’t necessarily increase the average range of the system.

Regardless of the range potential for certain weapon platforms, the human factor must be considered. Studies have shown that Soldiers can only consistently hit a human-size target more than 300 meters away 50 percent of the time or less on a qualification range. The numbers are significantly lower when a Soldier is operating in high stress environments. 
Therefore, whether a Soldier is firing a 5.56mm system with an effective range of 500 meters, or a 7.62mm platform with an effective range of 800 meters, what really matters is whether he or she has the skill to hit the target to begin with. Taking the human factor into account, one could argue that the “real world” effective range of a 5.56 system is similar to a 7.62mm weapon platform because the range potential of both platforms significantly exceeds the average Soldier’s marksmanship ability. This is not to say that exceptional Soldiers such as U.S. Army Snipers and Squad Designated Marksmen with specialized training are not fully capable of firing small arms to their maximum potential.

The value of having a system capable of increased range not only depends upon the skill of the operator, but it also depends upon the operating environment. In urban or restrictive terrain, for example, most line-of-sight ranges are significantly less than a weapon’s range potential. In more open terrain, the engagement range increase. For example, according to Lt. Col. Henthorn, in operating environments like Iraq, 80 percent of engagements are less than 200 meters. While in more distributed environments like Afghanistan, only 50 percent of engagements are less than 300 meters. 

What this is essentially saying is that the well-trained rifleman is effective out to 500 meters regardless of the caliber of rifle he is using, even though, in Afghanistan, approximately half of engagements occur beyond 300 meters. Given this, how would issuing GPC-caliber infantry rifles help the rifleman to be more effective?

The paper goes on to talk more about the general purpose round as they define it. Contrary to what Wr. Williams's citation implies, the author of the paper considers the M855A1 EPR to be a true general purpose cartridge, as it can engage a wide variety of targets reliably within the effective range of the rifle. This indicates that what Mr. Williams and the author of the paper (and, indeed, the US Army) mean by "general purpose" ammunition is different.

Regardless, I recommend that the reader follow the link and read the whole thing.

Wednesday, April 2, 2014

Momentum Has Nothing to Do With Stopping Power

There is a major misconception that pops up often in discussions of small arms: That momentum reflects in some way the terminal effect that a projectile has on a human target. It seems to be standard in the gun journalism industry when evaluating new calibers for game or war to test them against steel poppers, implying or even outright stating that this informs the terminal effect of the round. Even Larry Vickers, to whom I am not even close in terms of experience, says in this video about PDWs that the low momentum produced by the 4.6x30 round - making it unable to knock down the steel target - is a "clue" to low terminal performance.

Now, I have little expectation that a 4.6x30 round, which produces about 540J from the MP7, will perform much better against a human target or gel block than a 9mm JHP or even FMJ. It may more consistently perform after penetrating ribs, but in general, the round is limited in its effectiveness by its low muzzle energy, and its ability to deposit that energy in the target (link starts a download). However, is what Larry says true? Is low momentum a "clue" that a round might not have very good terminal effectiveness? Well, I don't really think so. Sure, a cartridge with marginal terminal effectiveness, like the 4.6x30, might have low linear momentum. However, a cartridge like .45 ACP, which in hardball form produces no greater energy than the 4.6x30, produces more than two and a half times the linear momentum; comparable to the much, much more effective 5.56mm round, in fact.

Because of all the variables involved in the problem of terminal effectiveness against human targets - including the target's mental state, the perceptions of the shooter, and most important, the location of the hit - it can be difficult to say what is and is not relevant to the total sum of terminal effect. However, momentum is one metric that can be discounted entirely. Consider that when a gun fires, it creates a force going in two directions, the bullet and gas going forward, and the firearm itself going backward. This force acts on both bodies over the same length of time - that is, however long (and a little after, due to muzzle thrust) the bullet is in the barrel. Because the forces pushing the bullet and gas out the barrel, and pushing the gun backwards against the shooter's shoulder are equal and act over the same length of time, the momentum of the sum of the bullet and the gas propelling it, and the rifle recoiling, is the same. This means that the momentum of the rifle recoiling into your shoulder as you fire will always be greater than the momentum of the bullet as it hits the target, for two reasons. First, because the gases escaping from the muzzle account for momentum lost, and because the bullet loses velocity - and thus momentum - as it flies downrange, whereas the rifle doesn't have to travel to recoil into your shoulder.

However, we observe as the unspoken first law of shooting that guns have a deadly end, and a non-deadly end. If momentum informed the terminal effect of a weapon against living targets, we'd all be dead fools.

So remember, the next time you're shooting silhouette targets with your .45 ACP 1911 and they fall with a satisfying "clunk" to the ground, the only game the momentum of that 230gr hardball ever felled were made of AR500 steel.

Check me out at The Firearm Blog!

About a month and a half ago, I was contacted by Steve of The Firearm Blog to re-post my article The Case Against A General Purpose Cartridge up at his website. After a short conversation, he decided to hire me on as a monthly writer. So far, I've written two articles for them, so my readers should go check them out!