Information on “stopping power”/”killing power” formulas

[Icehunter]

Hello everyone,

First let me say I hope everyone had a great holiday season and a great start to the new year! I posted this in the “general discussion” section because I couldn’t find anywhere else that seemed to fit. If there is a better location for this thread can someone please let me know? Thanks!

I’ve been playing around with a few of the published “stopping power” or “killing power” formulas and I am hoping folks can provide some more information. Basically I am looking for references/sources for the different formulas.

As background, I work in Arctic Canada doing scientific field research. Polar bears are a constant threat in our field camps. We generally carry pump-action 12 gauge shotguns loaded with slugs, and our research people are trained using the same guns. However lately I’ve been looking into buying a rifle to carry for personal protection and lethal defence against polar bears. I also field a lot of questions from other researchers on what caliber and ammunition combinations would be the best choice. A lot of people, for example, want to know if a 12 gauge with slugs is an effective choice, or if they should be carrying a rifle (as an aside, a slug is effective at close range, with lots of defence kills to show it, but I would personally prefer to carry a rifle). Please note that I don’t consider myself an “expert” on polar bears, firearms, killing power, etc, but I am a hunter, shooter, and gun nut. In comparison to many researchers who work in the north, who don’t hunt or shoot (many have never used a gun before they do the live-fire training), I guess I am an expert.

With this is mind, I tried to come up with an effective and objective (“scientific”) method of comparing the relative merits of different caliber/gauge and load combinations. Using the various formulas is about the only objective way to do this. So I used four different published formulas which I found on the internet to compare a bunch of different options. I wanted to come up with a comparison that would provide researchers with some basic information to guide their choice of polar bear defence firearm.

I am not going to get into the results here, but I can provide more detail if anyone is interested. I’m also not going to provide my ideas on which formulas work or don’t work, although I’d be happy to hear opinions on the different equations (they’re all different, and none are perfect!). What I am hoping to get is the information needed to cite the different formulas in a published paper or research document (I might try to publish my results in the scientific research journal Arctic, and to do so I need to extensively reference my sources).

I used the following four equations:

The Taylor Knock Out Factor – I have a good reference for this, from Taylor’s African Rifles and Cartridges book, but he also published an article in the November 1947 issue of the American Rifleman magazine. Does anyone out there have this article? If so, could you provide the reference (title and page numbers)?

The Optimal Game Weight (OGW) formula – I have a reference for this one as well, from the 47th Edition of the Lyman Reloading Handbook. However there was also an article published in the April 1992 issue of GUNS Magazine, and I am again hoping someone can provide the title and page numbers.

Wooters’ Lethality Index – this one has been published a few times, and I don’t have a good reference for it. I again am looking for page numbers and titles for the following articles:

- reference in the July/August 2005 issue of Rifle Shooter magazine
- January 1996 issue of Peterson's Hunting magazine (I think this was the original reference)
- A Guns & Ammo issue from the 'mid to late nineties'
- It was also used in an article called Cartridge Efficiency by George Calef in the March/April 2005 Rifle Shooter Magazine (however I have no page numbers) (this one may be the same as the first one noted above, although the month/issue is different – I found the info on different websites).

Thorniley (or Thornily?) Relative Stopping Power index – I have basically no information on this one at all, other than what is available on the Beartooth Bullets website (they have a calculator there for the formula). So for this formula I am essentially in the dark, and ANY information would be much appreciated.

I am planning to check my local public libraries but I don’t expect much success (I checked before and the city library system doesn’t have much for hunting and shooting magazines).

I know I’m asking for a lot of information/help here, and I apologize for posting such a long thread, but I could really use some help here! Thanks in advance everyone.

Regards,

Jeff Higdon
Wildlife Biologist
Winnipeg, MB, Canada

[Mohawk]

Hi, Jeff. A little off topic, but how to polar bears rank in agressiveness when compared with other bears?

[trotterlg]

These "formulas" just are about worthless I think.  They do not take into account the bullet type or how fast it is spun up, both of which make far more difference in what the bullet will do than just the weight and speed calculation.  If this is just a study of some sort then have at it, to see what really happens you just have to take a rifle and kill something you're self  to see how it works.  Math cannot solve all things hunting related, but if it is something that intrests you then go for it, I just think you will find calculations mostly worthless.  Take a gun, go shoot some animals and then judge for your self.  The articles were written to make money for the writer, they did that, whether or not they have any other valid purpose is not clear to me.  My advice to you is to stop reading and start doing, then you can write an article and become onte of the "experts".  Larry 

[deltecs]

These "formulas" just are about worthless I think.  They do not take into account the bullet type or how fast it is spun up, both of which make far more difference in what the bullet will do than just the weight and speed calculation.  If this is just a study of some sort then have at it, to see what really happens you just have to take a rifle and kill something you're self  to see how it works.  Math cannot solve all things hunting related, but if it is something that intrests you then go for it, I just think you will find calculations mostly worthless.  Take a gun, go shoot some animals and then judge for your self.  The articles were written to make money for the writer, they did that, whether or not they have any other valid purpose is not clear to me.  My advice to you is to stop reading and start doing, then you can write an article and become onte of the "experts".  Larry 

I believe this advice about shooting different game with different bullets to be most apt.  However, one cannot discount the experience from others who have had more experience on different game using different bullets for comparison, thus the derived formulas.   Polar bears are large dangerous game and need to be respected as such.  So, regardless of solid or expanding bullets, using formulas to get an idea of a good DG rifle cartridge is appropriate.  Any formula that is derived using momentum as part of the whole will usually give best idea of straight line penetration into the vitals for a hard hitting KO punch.  Momentum is velocity times bullet weight in grains divided by 7000.  The momentum values from this formula do not depend on whether the bullet is constructed of solid material or expanding.  A bullet having a higher momentum value will normally penetrate further and in a straighter line than one of less value, if using equivalent comparisons.  IE using Barnes X bullets compared to Barnes X bullets or similar.  Expanding bullets of like construction compared to like bullets from a different manufacturer.  The other important quality of a bullets KO power is its cross section or caliber whether or not expanding or solid.  So using Taylors KO formula incorporates both momentum and caliber.  Hatchers formula incorporates cross section instead of caliber to derive its KO results.  Same as Taylors but instead of bore diameter, Hatcher uses the bullets cross sectional area.  IE .308 Taylor bore area.  .308/2=.154 squared is Hatchers variation.  Momentum times the bore diameter is Taylors KO and Hatchers is momentum times bore radius squared.  Hatchers more accurately depicts the frontal bullets impact more accurately than Taylor for knock down impact power.  Beware of energy calculations as velocity is squared thus resulting in accurate but not effective terminal ballistics.  Check up on Kevin Robertsons book "The Perfect Shot"  He clearly explains terminal ballistics using both solid and expanding bullets on game and why some work so much better than others in plain language.  Hope this helps. 

[trotterlg]

I think this is an attempt to make Rocket Science out of common sense.  Big game = Big bullet, Small game = Small bullet.  This will probably work for about 99.9% of us.  If I were to be hunting something that wants to eat me, I would probably rely more on someones real experience with a bullet than on what a computer told me.  Larry

[deltecs]

I think in my previous post, I've related experiences from just those real hunters who have shot lots of DG game, seen and recorded the results; thus deriving these OGW, KO, or any other formula to relatively reflect a bullets terminal ballisitics on game for comparisons.  I'm sure most of these hunters have shot more big game and more DG game than almost anyone who posts on GBO, so I think I'd take their advice and experience into some account and not discount their conclusions or logic as BS.  One might have a better understanding of terminal ballistics of a bullet on game if they had read "The Perfect Shot".   This book was written by a pro hunter who also is a vet that did forensic exams on game after shooting them to determine the bullets effect on the animal.  It was written to provide hunters with a better understanding of African game anatomy for better shot placement and humane kills.  If one has not read it nor understand the terminal ballistics on game, I take these opinions with litte credibility. 

[trotterlg]

Guess I need to get one of them fromulas before I go out Coyote calling again to see if my 17 Remington can really kill one.    Larry

[Bigeasy]

Hello Jeff

Most of these formulas in one way or another factor in velocity, bullet weight, and sometimes bullet diameter.  None are particularly accurate, as those that put stock in velocity loose sight of caliber and bullet weight - The 22-250 has decent muzzle energy, but would be far inferior to say a 30-30 as a bear caliber.  The formulas that put a lot of stock into bullet weight and diameter fail to consider bullet expansion.  Modern, controlled expansion bullets such as the Barnes X Bullet can provide performance all out of perportion for a given caliber compared to a bullet of standard construction.

For self-defence against big bears, your requirements are different then those of a sport hunter.  You do not need the ability to snipe a bear at long range, you need to be able to stop a bear up close, and fast.  That means a big, heavy, controlled expansion bullet at moderate velocity.  To my way of thinking, that would mean a 375 H&H, a heavily loaded 45/70, or even a 416 Rem. or a 458 Win.  I would probably want a quality red dot sight, backed up with good open sights.  I would question the effectiveness/penetration  of a soft lead 12ga slug against a 1200 lbs. plus animal that has to be stopped right now.

Larry

[super mario]

heres a good read

http://www.rathcoombe.net/sci-tech/ballistics/myths.html

[Icehunter]

Thanks for the replies everyone. It took a while for this thread to get going, and it's been a while since I came back to check.

Mohawk - to answer your question, I don't think polar bears are generally more aggressive than grizz, or even the odd POd blackie. Some are very aggressive, some aren't aggressive at all. All depends on the bear, and how experienced it is with people. I think the biggest difference with polar bears is that they are really really persistent, and they'll come back to your camp over and over again, getting braver (but not necessarily more aggressive) each time. Blacks are easy to scare off, polar bears are not. Another big difference between grizz and polar bears are that the polar bear considers you to be food. Most attacks are predatory, the bear has decided it will kill and eat you. And when one does decide that you're dinner, nothing short of killing it will turn it away. (I've heard similar things about black bears, attacks are often predatory in nature, whereas a grizz attack is usually territorial).

Bigeasy makes an important point about the difference between a bear hunting rifle and a bear stopping rifle. Lots of my Inuit friends in the north use very small caliber rifles for polar bears, most are killed with 22-250s and the like (yes, they are crazy!). The legal minimum in Nunavut these days is a .243. Inuit hunters generally get really close to the bear and shoot for the ear or heart, most are one shot kills. I've heard many many legitimate stories of polar bears being killed by 22 LR, 22 Mag, even a one shot kill (heart shot) on a large adult male...with a 17 HMR!!!! I asked one friend how close he usually gets, his reply: "As close as I possibly can, and you better not miss!".

I would hazard a guess that most defence kills in the north have been done with a .303 British and FMJ military loads, simply because just about everyone up there has a military surplus SMLE (given to the Northern Rangers, a part-time military recon group comprised mainly of Inuit hunters - sort of like a reservist thing).

I agree that NONE of these formulas are perfect, and all have their biases based on what the author/developer thinks are important factors. Hence, Taylor's KO formula is calculating a very different thing than Wooters Lethality Index (my thought on this comparison, for polar bears, is that the TKO formula is a better representative of what is needed to stop an angry bear intent on eating you). The TKO and Thorniley formulas measure "stopping power", the other two measure "killing efficiency" (and yes, both are nebulous terms that aren't easily defined!).

WRT bullet construction/type, the literature on the formulas does usually (and explicitly) state that suitable bullet choice is assumed (i.e., you're using the right type of bullet for the application).

Shooting a bunch of different game with different bullets would be the best way to go, but there's no way I can go up north and shoot a bunch of bears, lol. I have done the next best thing, as others recommended, and that is to talk to folks that have. The polar bear protection folks I know (who work with problem bears, do guarding services for fieldwork crews, film crews, etc.) generally carry nothing smaller than a .375, and many prefer a .416 or .458 (exactly as Bigeasy suggested). One important suggestion I received from those folks is to check out the 35 Whelan in a pump-action or dependable semi - the advantage to a pump is that most researchers are already familiar with the action from their training programs using Remmy 870s and slugs. The advantage of a clean dependable semi is obvious - no one will short-stroke in an emergency situation. A recent article actually used the Wooters formula to conclude that the Whelan was the most efficient cartridge out there with respect to the amount of powder burned (or something like that).

I have been messing around with all four formulas, using ballistic info from the Big Three ammo companies only (most readily available, especially in remote areas, and the average researcher doesn't reload). I certainly wouldn't rely solely on the results to choose a caliber, but the results are instructive nonetheless. For example, until you get up to a .338 Win Mag, there is no real improvement of a rifle over a 12 gauge (i.e., 12 is just as effective as a 30-06 - again, let me stress, this is based on the formula results ONLY, I KNOW a 30-06 could be an effective bear killer at close ranges, but what I am saying is that it doesn't provide enough of a close-range advantage to justify buying one solely for bear protection if you have a dependable slug gun).

Personally, I'm now in the market for a decently-priced used 35 Whelan or a .375 H&H. A .338 Win Mag is also a possibility, I'm on a limited budget and I like the thought of getting something a little more versatile - I can use the Whelan or 338 for moose hunting, if I show up at moose camp with the .375 I'll be laughed out the door (we generally hunt moose with .303, .308,. 30-06, etc., which, interestingly enough, are way too small for moose according to all the gun writer "experts", I guess no one told Newfoundlanders that we're killing all our moose with "deer rifles", lol).

I have read alot of Kevin Robertson's work, but not The Perfect Shot (yet, it is on my list of books to purchase, along with Boddington's updated Safari Rifles).

Thanks for all the comments folks! regards,

Jeff

[Syncerus]

I'd try to pick up an old Ruger M77 (yes, pushfeed!) with a tang safety. Cut the barrel down to 20 inches, replace the irons with something good, and put it in a Ramline or similar ugly plastic stock. It's not horribly expensive and will do the job at 12 feet, if you have to use it. Keep it light; it's a carry gun, not a shooter. The Barnes X 350 gr at 2400 fps will work nicely, but about any .458 ammo will do. Why screw around with something smaller?