CH: You mean a government study was somehow flawed? I find that surprising!
In a word, "yes".
Below is the analysis I did back in September of 2003.
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Safety in Bear Country: Protective Measures and Bullet Performance at Short Range
General Technical Report PNW-152
http://www.fs.fed.us/pnw/pubs/gtr152.pdf * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
The study is dated (1983) and the methodology used to calculate the results is horribly flawed, but the raw data is raw data. I entered that data into a spreadsheet and made my own calculations, with drastically different results. More about my results later, but first, some excerpts regarding the report’s methodology, and a few comments about its flaws:
We evaluated each cartridge-bullet weight-barrel length combination tested by four ballistic categories: striking energy, penetration, retained bullet weight, and bullet expansion. We also measured bullet velocity because energy is a function of bullet weight and velocity.
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To determine expansion, we measured to the nearest 0.01 inch the maximum diameter of the bullet (or the largest fragment) and the diameter at 90 degrees to the maximum diameter. The cross-sectional area of this ellipse was determined by the formula A=3.1416 ab, where a = maximum diameter and b = diameter at 90 degrees to a. Both retained bullet weight and expansion were expressed as a percentage of the weight and cross-sectional area of an unfired bullet pulled from a cartridge identical to that fired in the tests.
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Because we had no unbiased way to determine the relative importance of each ballistic category, we considered each to be equally important. Our first step in evaluating overall ballistic performance was to calculate the average value in each category for the three shots fired from each test combination. We then divided each average by the maximum average value in its category to convert it to a relative proportion of the maximum value encountered during the tests. We rounded the quotient to two significant decimal places and multiplied by 100 to eliminate decimals. This transformation also eliminated the different category units and allowed all four to be arithmetically combined into a single performance score. We calculated this score by multiplying the four relative scores of each test combination. To eliminate the use of unwieldy eight-digit numbers as scores, we divided the product by 100,000 and rounded the quotient to the nearest whole number. This provided a two- or three-digit score for each test combination, which we ranked in highest to lowest order.
Your government funded study can’t get the formula for the area of an ellipse correct, but there are even bigger problems. Accepting their definitions for ‘A’, ‘a’ and ‘b’, where ‘a’ and ‘b’ are diameter measurments, the correct formula is “A=3.1416 * 1/2a * 1/2b”, not “A=3.1416 a * b”. The formula error resulted in a calculated expansion that was 4x greater than it should be, and erroneously skewed the results in favor of expanding bullets regardless of their initial or final diameters.
Further, the authors don’t seem know the difference between “retained bullet weight” and “
percent retained bullet weight”, or between “bullet expansion” and “
percent bullet expansion”.
Consider the following bullets:
.224” 55g, expanded 100% to .448” and retained weight of 100% or 55g, and
.458” 405g expanded 64% to .750” and retained weight of 90% or 364g.
Using the author’s methodology and assuming expansion in a perfect circle, the .224” bullet would score 100 in both retained weight and expansion, while the .458” bullet would score 64 and 90 respectively. These interim scores are then multiplied together (along with those for striking energy and penetration, which we will ignore for now) to achieve a final score. Hence the .224” bullet scores 10,000 while the .458” bullet scores 5,760, or a little over half what the .224” bullet scores in these categories. The author’s methodology resulted in silly stuff like a 7x57 Mauser with a 175 grain bullet with a retained weight of 91g outscoring a 12 gauge 438g slug with a retained weight of 420g, even though the slug out-penetrated the 7mm bullet. The problem is exacerbated due to the author’s use of an incorrect formula for calculating the area of the expanded bullets, as previously explained.
It seems to me that it would make much more sense to compare
retained weight in grains, not percent, and
bullet expansion in inches instead of percent, and base the scores accordingly. In this manner, the .224 scores 55 and .448, which combine to form a score of 25.19, while the .458” bullet scores 364 and .75, for a combined score of 273. I think most of us would agree the .45-70 is more likely to be 10 times more effective than a .22-250 for the purposes cited, rather than half as effective, so this methodology at least passes the laugh test.
I used this method to recalculate scores for all the loads tested in the report, along with some Garrett Hammerhead loads and loads based on handload data.
Here are the
US Forest Service Results:
Cartridge/Notes....USFS Score....USFS Rank....Weight (grains)....Type....Brand....Velocity @ 15 Yards (fps)....Energy @ 15 Yards (fpe)
.458 Win. Mag.............538.....1....510....RSP....W-W....2074....4871
.460 Why. Mag.............467.....2....500....RSP....WBY....2364....6204
.375 H&H Mag. (L).........301.....3....300....SSP....W-W....2541....4903
.338 Win. Mag. (S)........260.....4....300....RSP....W-W....2314....3568
.375 H&H (L)..............239.....5....270....RSP....R-P....2659....4241
.338 Win.Mag. (S).........213.....6....200....PSP....W-W....2699....3235
.338 Win. Mag. (S)........197.....7....250....SSP....W-W....2507....3491
.338 Win. Mag. (L)........191.....8....200....PSP....W-W....2634....3563
.338 Win. Mag. (L)........186.....9....300....RSP....W-W....2360....3710
.375 H&H Mag. (S).........185....10....300....SSP....W-W....2401....3843
.30-06 U.S................157....11....220....RSP....R-P....2261....2498
.30-06 U.S................153....12....180....RSP....R-P....2456....2411
.444 Marlin...............146....13....240....FSP....R-P....2237....2668
.358 Winchester...........142....14....200....SSP....W-W....2366....2488
7mm Rem. Mag.............141....15....175....PSP....W-W....2709....2853
.375 H&H (S)..............137....16....270....RSP....R-P....2456....3735
.45-70 U.S. (S)...........133....17....300....HSP....FED....1573....1649
.308 Winchester...........128....18....180....RSP....FED....2430....2360
.45-70 U.S. (L)...........124....19....300....HSP....FED....1666....1849
.358 Norma Mag............115....20....250....PSP....NOR....2730....4139
8mm Rem. Mag..............107....21....185....PSP....R-P....2991....3676
.300 Weatherby Mag........104....22....180....PSP....WBY....3033....3678
.338 Win. Mag. (L)........100....23....250....SSP....W-W....2594....3735
.350 Rem. Mag..............93....24....200....SSP....R-P....2568....2931
7x57mm Mauser..............87....25....175....RSP....FED....2419....2274
12-gauge x 2-3/4 inch......74....26....438....LRN....FED....1398....1902
.45-70 U.S. (L)............65....27....405....RSP....R-P....1322....1572
.300 Win. Mag..............60....28....200....PSP....FED....2699....3237
.300 Weatherby. Mag........59....29....220....RSP....WBY....2798....3826
.45-70 U.S. (S)............50....30....405....RSP....R-P....1211....1319
8mm Rem. Mag...............49....31....220....PSP....R-P....2779....3773
.44 Rem. Mag. (L)..........47....32....240....LGC....R-P....1401....1046
.300 Win. Mag..............44....33....180....PSP....FED....2959....3268
Here are
my results, based on ADDing the individual scores (Additive Rank) for energy, penetration, retained weigh and expansion. (Since I didn’t have weight retention and expansion data for the new loads, I used the averages for the original four .45-70 loads.) I also included a “Multiplier Rank” based on my methodology, which corresponds closely but not exactly to the “Additive Rank”:
Cartridge/Notes....Weight (grains)....Type....Brand....Velocity @ 15 Yards (fps)....Energy @ 15 Yards (fpe)....Multipier Rank....Additive Rank
.458 Win Mag...............510....RSP..........W-W........2074....4871......1.....1
.460 Why. Mag..............500....RSP..........WBY........2364....6204......2.....2
.45-70.....................540....HC...........Garrett....1550....2880......3.....3
12-gauge x 2-3/4 inch......438....LRN..........FED........1398....1902......9.....4
.45-70.....................400....JFP..........Speer......2002....3560......4.....5
450M.......................400.....JFP.........Speer......1958....3405......5.....6
.45-70.....................420.....HC..........Garrett....1850....3200......6.....7
.375 H&H Mag. (L)..........300.....SSP.........W-W........2541....4903.....11.....8
.45-70.....................350.....JSP.........Hornady....2191....3730......7.....9
450M.......................350.....JSP.........Hornady....2196....3747......8....10
.45-70.....................300.....Partition...Nosler.....2424....3914.....10....11
.45-70.....................420.....HC..........Garrett....1650....2450.....13....12
450M.......................300.....Partition...Nosler.....2321....3588.....12....13
.45-70 U.S. (S)............300.....HSP.........FED........1573....1649.....18....14
.45-70.....................300.....Nosler Par..Garrett....2150....3080.....14....15
450M.......................250.....XFN.........Barnes.....2509....3494.....15....16
.338 Win. Mag. (S).........300.....RSP.........W-W........2314....3568.....17....17
.375 H&H (L)...............270.....RSP.........R-P........2659....4241.....16....18
.45-70 U.S. (L)............300.....HSP.........FED........1666....1849.....20....19
.45-70 U.S. (L)............405.....RSP.........R-P........1322....1572.....23....20
.45-70 U.S. (S)............405.....RSP.........R-P........1211....1319.....28....21
.375 H&H Mag. (S)..........300.....SSP.........W-W........2401....3843.....19....22
.338 Win. Mag. (L).........300.....RSP.........W-W........2360....3710.....22....23
.444 Marlin................240.....FSP.........R-P........2237....2668.....21....24
.338 Win. Mag. (S).........250.....SSP.........W-W........2507....3491.....24....25
.338 Win.Mag. (S)..........200.....PSP.........W-W........2699....3235.....25....26
.358 Norma Mag.............250.....PSP.........NOR........2730....4139.....30....27
.338 Win. Mag. (L).........200.....PSP.........W-W........2834....3563.....26....28
.375 H&H (S)...............270.....RSP.........R-P........2456....3735.....27....29
.30-06 U.S.................220.....RSP.........R-P........2261....2498.....31....30
.338 Win. Mag. (L).........250.....SSP.........W-W........2594....3735.....32....31
.358 Winchester............200.....SSP.........W-W........2366....2488.....29....32
8mm Rem. Mag...............185.....PSP.........R-P........2991....3676.....37....33
.300 Weatherby Mag.........180.....PSP.........WBY........3033....3678.....39....34
.30-06 U.S.................180.....RSP.........R-P........2456....2411.....33....35
.300 Weatherby. Mag........220.....RSP.........WBY........2798....3826.....41....36
7mm Rem. Mag..............175.....PSP.........W-W........2709....2853.....38....37
.350 Rem. Mag..............200.....SSP.........R-P........2568....2931.....34....38
.44 Rem. Mag. (L)..........240.....LGC.........R-P........1401....1046.....36....39
.308 Winchester............180.....RSP.........FED........2430....2360.....35....40
.300 Win. Mag..............200.....PSP.........FED........2699....3237.....43....41
8mm Rem. Mag...............220.....PSP.........R-P........2779....3773.....42....42
7x57mm Mauser..............175.....RSP.........FED........2419....2274.....40....43
.300 Win. Mag..............180.....PSP.........FED........2959....3268.....44....44
My results aren’t perfect either, as the .300 Win Mag 180g bullet comes in dead last, but I think the overall results make far more sense than what the USFS concluded.
Although I determined the methodology first and built my spreadsheet accordingly (rather than build the spreadsheet to make the numbers come out a particular way), I was not surprised the .45-70 did better than in the USFS study.
What did amaze me was 16 of the top 17 rankings went to a .458” bullet or bigger (12 gauge), and included ALL the .45-70 and 450 Marlin loads, even the original .45-70 loads tested by the USFS. The lone exception was a .375H&H load that came in at #11 (Multiplier Rank) or #8 (Additive Rank).
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There is no doubt that one could spend more time on the subject and come up with better ways to rank the various loads based on the given data. I've thought about doing it myself, but, frankly, I have better things to do. If anyone else is so inclined, I'd be interested in their results.
