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Sir Charles,

I see that you too are deserving of the "Rocking NF" brand.
Where do we get a cattle brand like that ?

[Linked Image]


Ron aka "Rip" for Riflecrank Internationale Permanente
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Lethality Indices of Art Alphin:

"Penetration Index" = PI = (KE/CSA) x (Sectional Density)

"Shock Power Index" = SPI = KE x CSA

where
KE = Kinetic Energy of bullet
CSA = Cross-sectional Area of bullet
M = Mass of bullet
V = Velocity of bullet
D = Diameter of bullet
N and Z = numerical constant factors for converting between Sectional Density (square bullet convention proportional to reality) and CSA (round bullet reality) for a particular "Index" formula
N is used for PI formula
Z is used for SPI formula

So by the same reduction to factors as I have been foisting on Sir Bob:

PI = N(M^2 x V^2)/ (D^4) = Momentum squared divided by bullet diameter to 4th power and all that multiplied by a constant numerical factor.

SPI = Z(MV^2)/(D^2) = Kinetic Energy divided by bullet diameter squared and all that multiplied by a constant

Such is the genius of Art Alphin, who claimed he got a Bachelor of Science degree in "weapon systems engineering" from West Point.
During the brief time I attended West Point (until they quit Vietnam and I quit them), there was no such degree.
There were no majors then, just an all-purpose BS from West Point.
Art designed the SAAMI .458 Lott throat with his advanced BS.


Allow me to suggest a new Lethality Index = SquareRoot[PI x SPI] = BS2 Index

BS2 Index = Square Root of [N x Z x M^3 x V^4 / D^2]

BS2 Index = (New Constant) x (Square Root of bullet Mass) x (Kinetic Energy at Impact) / (bullet Diameter)


Ron aka "Rip" for Riflecrank Internationale Permanente
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So Art's Penetration Index basically boils down to Momentum applied per unit of cross-sectional area of bullet,
with the depth of penetration arising from that being proportional to sectional density of the bullet.
Sectional density drives penetration for any given "Momentum-Squared" value.
This basis on momentum occurs even though the calculation is based on a Kinetic Energy value.
Seems this would be good only for nondeforming solid bullets stable enough to stay on course.

Art's Shock Power Index reflects the amount of KE applied to the bullet's CSA imprint on the target at impact.
Basically how hard it smacks the surface at impact.
So characteristics of both the bullet and the impact medium come into play regarding wounding effectiveness.
Seems like it would be applicable for comparing only bullets of the same type soft point construction.

A Unified Field Theory of Lethality Indices is needed to index for a combined penetration and smackdown potential for any bullet.

I am going to fiddle with BS Index, GW Index, and BS2 Index as well as Sir Bob's Latest TE adventures.

The "BS2" Index acronym stands for Bullet Swag Too/Also/2.


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Gentlemen,

I have an update for you all.
I loaded a couple of empty cases with 74gn of BENCHMARK powder instead of 75 behind the 450gn Hydro - and in my 24" barrelled Zastava the velocity was the same!
Just thought that I'd share that in case someone wants to duplicate my load.
I've since loaded a couple with 73gn and I'll keep you posted on how that goes...

Russ


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Originally Posted by BadboyMelvin

Gentlemen,

I have an update for you all.
I loaded a couple of empty cases with 74gn of BENCHMARK powder instead of 75 behind the 450gn Hydro - and in my 24" barrelled Zastava the velocity was the same!
Just thought that I'd share that in case someone wants to duplicate my load.
I've since loaded a couple with 73gn and I'll keep you posted on how that goes...

Russ


Sir Russ, you have found the 'accuracy node'......those loads should shoot very well, as is often the case with the 458 WM, it's a lot more accurate than it needs to be, good stuff Gentlemen. cool


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Originally Posted by Riflecrank
'Ernest Hemingway’s friend A.E. Hotchner once described a “yellowed four-by-five picture of Ernest,” shown him by Hemingway,
“aged five or six, holding a small rifle. Written on the back in his mother’s hand was the notation,
‘Ernest was taught to shoot by Pa when 2½ and when 4 could handle a pistol.’”
Firearms and shooting infused Hemingway’s existence and thus his writing ...'

[Linked Image]

Hemingway tops Sir Jerry for early age to start shooting.
Wasn't Hemingway's Pop a medical doctor ?
My how times have changed !
Good medicine and education back then is child abuse now.

Speaking of education, reminds me of higher math being practiced over at Sir Bob's latest blog:

https://bigborefan.wordpress.com/2021/09/11/a-reworked-te-formula/

Sir Bob:
If you multiply KEI by MF (your modified TKO containing M, V, and both CSA and sectional density {the M/CSA equivalent} as multipliers, instead of caliber alone),
your new TE ends up being momentum cubed with some manipulation by constants for manageable numerical value:

TE = (M^3)(V^3)/N




Sir Ron, I don't claim knowledge of advanced math - that's obvious! I graduated from highschool, grade 12, with top honors in my class, but only did a total of six math courses, including trig and physics at that level, and they were my best grades. The only math I've done since was related to optics for telescope making in changing a spherical mirror to a parabolical shape. And five years of post secondary never included one math or science course - to my regret. So you've got me on that one.

But I'm convinced that the TKO formula is flawed as it stands. The reasons are logical. For example: If a 400gr, .416 caliber bullet impacts an animal with the same momentum as a 400gr, .458 caliber, the TKO formula gives an advantage to the .458 caliber (We could specify the numbers but that doesn't make any difference in the outcome as to momentum. But SD does! The 400gr - .416" has an SD of .330 while the 400gr - .458" has an SD of .272. IF the bullets have the same structure and profile it's logical to assume that the .416" will penetrate deeper while the .458" will make a larger cavity. It appears that could be a "write off! No? BUT, if a 500gr - .458" is used producing identical momentum then that "wins" due to it SD of .341, PLUS its CSA of .165 sq in versus .136 sq in, by which the .458 should penetrate at least as deeply as the 400gr, .416". At least that's my logic, and I think from research it works something like that. The advantage the .458 has over the .416 is not only in CSA but SD and probably momentum, depending on the MV of each. And that's assuming equal structure (either soft or solid) and profile. But the exception is IF penetration is complete for each, then the .458 wins regardless of KE or momentum. In such cases CSA wins. Yeah, I know there are some "what ifs".

Is my logic wrong? But I defer to you in "advanced math"!

Bob
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Sir Bob,

I gave up on lethality indices a long time ago, but you have rekindled the interest.
I never added the down range effects of BC for soft point loads, but lookout now, I got the itch!

Of course the Taylor KO has limits, and was only ever meant as a rough judge at efectiveness in knocking an elephant down
with a close miss of the brain on a head shot.
To me that means it should only be applied to solid bullets,
because that is the only type of bullet that should be shot into the skull of an elephant.
Also limited to the recommended DG rifles of the day, probably .366 to .622 caliber, from 9.3x62mm Mauser to .600 NE.
No needle-like flechettes at hyper velocity, nor manhole covers dropped on an elephant's head from a few inches above.

The TKO of a 50-pound, 25"-diameter manhole cover moving at 1 fps is huge ! TKO = 1250 exactly.
Compare to the 300-gr .375-cal at 2500 fps: TKO = 40 or 40.1 depending on how precise you need to be.
Or the 900-gr .622-cal at 1950 fps: TKO = 156.

OK, surely any lethality index has got to have limits on the projectile caliber it is applied to.

I am going to come up with one that may be arbitrarily applied to the bracket from .308-caliber to .458-caliber,
and bullet weights and muzzle velocities those calibers get routinely hunted with, using soft points.
We all know the .458 WinMag is more than big enough for any game animal that walks the planet,
and a .30-06 with the right bullet will do for the lower end of the spectrum of game weight.

Kinetic energy is not the answer. Much of it goes into noise and temporary wound channel and heating the meat.
Too much wasted sound and fury.
Momemtum is conserved in a more friendly-to-the-SWAG way.
Energy is conserved but kinetic energy evaporates into many other forms of energy.

Mass, caliber, velocity, and how they relate through sectional density and ballistic coefficient, that's the ticket
for my SWAG via KISS principle.

"Ballistic Product" (BP) is my new accounting method.
It is simply the product of 4 factors. Cute, eh ?

BP = (Bullet Weight in grains) x (bullet Velocity in fps) x (bullet caliber in inches) x (sectional density as based on pounds of bullet per square bullet CSA sq.in.)

BP = W x V x C x Sd

BP is numerologically cumbersome, too big, so it is converted to a unitless index by dividing it by 84,000.
That is arrived at by using 7000 grains per pound and 12 inches per foot: 7000 x 12 = 84,000

Ballistic Product Index = BPI = (BP / 84,000) = (W x V x C x Sd) / 84,000

Now we are cooking.

The final touch from Sir Bob's tutelage is to make it the "Terminal Ballistic Product Index" (TBPI)
by using impact velocity at locations downrange from the muzzle.
That's how BC gets involved.

But first I must start by calculating some TBPI at the muzzle velocity.

As Sir Bob said, we have to make our rough comparisons when using any index
by sticking with similar bullets by type of construction of the soft point bullet.
It is impossible to control for live game tissue impact due to its constantly changing state.
This is like horse shoes and hand grenades in many ways.


Ron aka "Rip" for Riflecrank Internationale Permanente
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TBPI = 0.500 ... .30-06 Hot Load: (180 gr)x(2800 fps)x(.308 cal)x(.271 Sd) / 84,000

TBPI = 1.00 ... .375 H&H mild load: (300 gr)x(2450 fps)x(.375 cal)x(.305 Sd) / 84,000
TBPI = 1.06 ... .375 H&H hot load: (300 gr)x(2600 fps)x(.375 cal)x(.305 Sd) / 84,000

TBPI = 2.00 ... .458 WinMag SAAMI load: (500 gr)x(2150 fps)x(.458 cal)x(.341 Sd) / 84,000

Just to show how an extra 200 fps of velocity affects the TBPI with same 500-grainer, consider the .458 WM+ at 2350 fps:
TBPI = 2.18

For the 400-gr/ .458-cal bullet: In .45-70 Gov't., .458 WM, .458 WM+, or 460 Wby:

1800 fps TBPI = 1.06
2000 fps TBPI = 1.19
2200 fps TBPI = 1.31
2300 fps TBPI = 1.36
2400 fps TBPI = 1.42
2500 fps TBPI = 1.48
2600 fps TBPI = 1.54
2900 fps TBPI = 1.72

So a .375 H&H is twice a .30-06, and about equal to an Elmer Keith .45-70 Gov't. lever action load.
A SAAMI .458 WinMag 500-grainer is about double the .375 H&H.
Sounds about right. Must be a numerological God wink.

Next will figure a Sir Bob like relation of TBPI to optimum game weight downrange using BC for bullets of
different caliber and same soft point type, like a Woodleigh PPSN for all ...


Ron aka "Rip" for Riflecrank Internationale Permanente
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Thanks Sir Ron... I knew you could do it if anyone could!

Bob
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Good thought and clear presentation Sir Ron. Well done.

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Bullet Weight Velocity Caliber SD Constant TBI Yards
480 1950 0.458 0.341 84000 1.740269143 0
180 2750 0.308 0.271 84000 0.491865 0
275 2550 0.338 0.345 84000 0.973485268 0

480 900 0.458 0.341 84000 0.803201143 300
180 1750 0.308 0.271 84000 0.313005 450
275 1500 0.338 0.345 84000 0.572638393 450
Had to guess at the Yardage vs. Velocity but built a little spreadsheet using three Cartridges that I have killed a few things with, it is pretty interesting.

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Sir Dennis,

Buy a donkey for those flowers.

You did get the 480-gr/.458-cal SD switched for the 500-gr SD, however.
480-grainer SD is 0.3268978 or 0.327 for our purposes.
500-grainer SD = 0.341

So for 480-grainer at 1950 fps MV from the .458 WinMag,
TBPI-M = 1.669

I think you underestimated the 300-yard velocity a bit for the 480-gr/.458-cal.
It might be closer to 1300 fps and quite Bagwellian at 300 yards.
If so,
TBPI-300y = 1.113
If that is your hardcast FN from your .458 WinMag, it would do well on elk if placed well at 300 yards,
like a hot Bowie knife in butter.

This suggests possible matching of TBPI to game weight.
I am open to suggestions.

First I think we should consider the deer rifle.
The .30-30 WCF has worked pretty well as a deer rifle.

The 170-gr/.308 Winchester Silver Tip seems to be good for deer with minimum fuss (BC = 0.255, SD = 0.256)
or the 170-gr Nosler Partition "flat point" with identical BC, and SD, of course:
2200 fps is for a 24" barrel.
Let us say MV is 2100 fps for the most common 20" lever action that has performed so well with that Winchester factory load.
Limiting it to 200 yards or less is best.

TBPI-M = 0.335
TBPI- 50y = 0.311
TBPI-100y = 0.288
TBPI-200y = 0.246

Maybe we say a TBPI of about 0.300 is a good deer cartridge ?
Maybe we say that TBPI x 1000 = optimum game weight in pounds with good shot placement and good bullet ?
The trusty thutty-thutty is good for a 311-pound deer at 50 yards, a 288-pound deer at 100 yards, etc.

So your .458 WinMag with 480-grainer at 1950 fps MV will handle a 1600-pound bison at spitting distance.
Nice 5-1/2 y.o. herd bull would make lots of burger, a robe and skull.

Just a suggestion for now, pending further considerations.

Maybe for DG we say that optimum game weight is TBPI x 666 pounds, the mark of the beast.
If you run out of soft point TBPI for really big DG then you switch to nondeforming FN solid bullets and let the devil worry about TBPI ?


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So John55 coaxed me into getting some REAL bullets for my 458 and I ended up with a box of 500 grain Swift A-Frames. Any sorta input for that one? I have RL7, H322, H4198 and some others that should work fine with the big guy. Not looking for every last FPS from it, just something to play around with in the back yard.


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Yep. Just borrowed your sd number and made a poor guess on remaining velocity. Ran some numbers later and still have twice the tbi at 450 than the trusty ‘06.
I’ve shot a lot of rocks at that distance and those big flat nosed slugs land hard.
Best to you sir!

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Sir Scotty,

I have a couple boxes of Swift A-Frame .458 -cal, old production from about turn of century.
One box each of 500-gr and 400-gr.
The bullet overall lengths of those old ones are 1.400" and 1.170" respectively, within +/- 0.005"
with their flat lead meplats topping off the semi-spitzer ogives.
The nose projections of those bullets are respectively 0.785" and 0.685" ahead of the cannelures.
The cannelures are about 0.070" broad in length of run on the shank, 0.445" diameter.

Looking at SWIFT BULLET COMPANY RELOADING MANUAL NUMBER TWO of 2014,
The A-Frame 500-grainer is 1.430" long with BC = .361
450-grainer is 1.310" long with BC = .325
and 400-grainer is 1.130" long with BC = .258 (bigger exposed lead flat for tubular magazine use).
That is a little different from my old ones which will be reserved for Bobbed Bullets, Ltd. R&D.

The manual does show a RL-7 load for the 500-gr A-Frame in the .458 WinMag.
That powder is a little on the fast side for top velocity at low pressure, but here it is,
for a 24" barrel, F-215 primer, and Federal brass, 3.340" COL or less, and 60,000 psi or less:

500-gr A-Frame:
RL-7
56.7 grains >>> 1910 fps (start)
61.0 grains >>> 2037 fps (maximum) with LR/net filling = 90%.

Six powders were shown for this bullet: H-335, H-4895, RL-7, RL-15, IMR-3031, IMR-4895.
I prefer the H4895 load:

500-gr A-Frame:
H-4895
66.0 grains >>> 1964 fps (start)
71.0 grains >>> 2112 fps (maximum) with LR/net filling = 104% (mildly compressed)

Or use the .458 Lott loads from the manual, always a safe starting place and easily surpassed, with the .458 WM+.
I don't expect high velocity at low pressure from Swift A-Frames, with their sticky-copper, full-bearing shanks,
I just expect boringly reliable terminal performance and good accuracy for one-shot kills.
Speaking of terminal bullet performance (TBP)
I gotta get back to crunching numbers for TBPI ... Terminal Ballistic Product Index. Yawn.
Real or phony, TBPI for soft point bullets is probably no worse than TKO for solid bullets.
Not all bad.


Ron aka "Rip" for Riflecrank Internationale Permanente
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Thanks RC, I’ve got H4895 as well so that will get tried. Thanks for the word on it.

I need to collect some more water jugs and try to catch one of them big devils.


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Bullet Weight Velocity Caliber SD Constant TBI Yards
480 1950 0.458 0.327 84000 1.668821143 0
180 2750 0.308 0.271 84000 0.491865 0
275 2550 0.338 0.345 84000 0.973485268 0

480 1100 0.458 0.327 84000 0.941386286 450
180 1750 0.308 0.271 84000 0.313005 450
275 1500 0.338 0.345 84000 0.572638393 450

Fixed it Sir.

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Popping back in Sir Ron to say; I think Mr. Bagwell proved that a big lead .458ish slug will kill them as far as you can hit them well and he started his at 1300 fps or so. The buffalo hunters of old would double lung from quite a ways off. Doesn't result in a DRT but was efficient. I would have no qualms about poking one at 250 yards and that limit is my confidence about hitting the spot every time. There was only one Saint Bagwell. smile

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Sir Ron,

Multiply by 2500 and you'll be about right.

A .30-06 firing a 180gr NP at 2750 should be capable for a 800 + lb moose at 400 yds with the bullet placed in vitals. Under my hunting conditions that 180 with a .474 BC would still be making around 2050 fps at 400 yds. In multiplying by 1000 that would be a calf moose! Many adult moose have been taken at 400 using a .30-06. 1 shot? 2 shots? 3 shots. Dunno, but the CO who taught seminars on moose hunting, and suitable rifles, claimed 2 ft-lbs per pound of weight was adequate assuming a proper hit. But, of course, adult moose vary greatly in size and weight from about 700 lbs to 1400 lbs! So 2050 fps at impact = 1680 ft-lbs/2 = 840 lbs. Also, a young man in Penn State killed a 700 lb black bear with his 30-30, and 1 shot! So 180x 2050x.308x.271 /84000 = .367 (close enough) x 2500 = 916 lbs (close enough?) Then, we had a native guy as a border attending college here. He and family were moose hunters (when ever they wanted) and he claimed to have killed an adult bull at 400 yards using 180gr Rem Core Lokts. He also loaded his bedroom with "illegal" cigarettes and boxes of .30-06, 180gr Core Lokts (He had a business going at home for the community + a maple syrup business!)

Just some thoughts for your computer... and I'm reworking my thoughts on TE. My new "new" formula would work out to 968 lbs... Ha! Written with erasable ink!


Bob
www.bigbores.ca

Last edited by CZ550; 09/16/21.

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Bob an adult Alaskan Yukon bull moose can weigh clos to a ton

Last edited by jwp475; 09/16/21.


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