Statistical Analysis of "Energy Transfer"

Discussion in 'Handguns: General Discussion' started by RyanM, Mar 29, 2005.

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  1. Zak Smith

    Zak Smith Moderator Emeritus

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  2. coylh

    coylh Member

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    Hi Zak! Yeah, I used your page. I've been using www.firearmstactical.com and the Street Stoppers book also.
     
  3. Zak Smith

    Zak Smith Moderator Emeritus

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    Anybody who really wants to understand modern terminal ballistics should read the published research on the subject (ie, papers), and contact an expert like Dr. Gary Roberts for more leads.
     
  4. lbmii

    lbmii Member

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    There might be a flaw in your calculation of wound volume that may throw quite a few things off.

    Let us say you have two bullets with identical diameters at the end of their penetration of gelatin. And let us say that both bullets had identical energy levels. And let us further say that Bullet A expanded slowly and penetrated 10 inches and Bullet B expanded very quickly and only penetrated 8 inches. Let us also say that the measured real volume of the two wound paths are very close in volume with Bullet A wound path narrower but deeper and Bullet B wound path wider and shorter.

    Using your formula below:

    PI * (D/2)^2 * P
    Where D is expanded diameter and P is penetration depth

    Bullet A the slow expanding deeper penetrating bullet will be granted a much higher wound volume than the rapidly expanding but shallower penetrating Bullet B.

    Now this is just speculation on my part. But would not this method of wound volume calculation give improper favor to slower moving (thus lower energy) bullets that might tend to open up slower and give disfavor to fast (high energy) bullets that might tend to open up faster during their gelatin penetration?

    Let us say Bullet C is slow and heavy and of a fairly low energy and penetrates 10 inches and expands slowly to 0.5 inch in diameter. Let us say that Bullet D is fast and light and has a fairly high energy and penetrates 10 inches but had quickly expanded to a 0.5 inch diameter early in its’ penetration of the gelatin. Bullet D would in reality have a higher wound volume than Bullet C.

    Your chart in the above scenario would show a lower energy bullet having the same wound volume as a higher energy bullet when in reality that would not be the case.
     
  5. coylh

    coylh Member

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    Yeah, that's the complaint about the cylinder aspect. The ideal bullet for "cheating" the index is a small, extremely heavy bullet that penetrates as much as possible before blossoming into the widest final diameter right at the end of penetration.
     
  6. RyanM

    RyanM Member

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    That's why I limited my plots to handgun bullets. Rifle bullets usually make really big holes, and can have variable expansion rate. But pistol bullets pretty much all expand within about an inch or so of penetration.

    Yes, I know either Sanow or Marshall said that bullets like the Black Talon expand slowly. That's BS (especially in the case of the Black Talon, which expands very quickly). Almost all handgun bullets will be fully expanded within a very short penetration distance. That's one of the assumptions which MacPhereson made when he plotted the penetration curves in Bullet Penetration (which I really wish was still in print :( ), and those curves tend to be quite accurate for pistols.
     
  7. griz

    griz Member

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    Thanks Ryan for the information and a great thread. I had assumed that the the tears in gel equated to more damage in tissue, but your expanation makes sense.

    One more question. What is your source for the comment that pistol bullets expand to final diameter within a short time? The only way I can imagine knowing that would be high speed video, but I simply don't know. The reason for my question is I have recovered (rifle) bullets from deer that had the jacket adjacent to, but seperated from, the core. That can only happen with expansion happening near the end of travel.
     
  8. RyanM

    RyanM Member

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    Either Dr. Fackler or MacPhereson did some high speed photography tests, I believe. And logically, a pistol bullet is really incapable of expanding very slowly.

    Expansion of a hard material like lead (it's soft as metal goes, but compared to your guts, it's pretty darn hard), requires tremendous pressure, which requires very high velocity. Pressure is the highest earliest on in the penetration, since the bullet loses velocity from there on in. At pistol starting velocities, after a couple inches of penetration pressure on the bullet is so low that the lead can't deform any further no matter what, anyway.

    Between "thought experiment" analysis, and some high-speed photos, it looks like that for the most part, if a pistol bullet hasn't expanded in the first couple inches, it's never going to expand, and whatever diameter a bullet has attained after a couple inches is what it's going to stay at.

    Like Federal boasts that the Hydra-Shok is fully expanded after 2" of jello, and has a bunch of high-speed photos of Hydra-Shoks coming out the back of 2" jello blocks. There's really nothing special about the Hydra-Shok that allows it to expand so fast; most handgun bullets can, too. That's just Federal capitalizing on the BS that Marshall and Sanow have spread.

    In the high-speed photo here http://www.remingtonle.com/ammo/gshpj.htm you can see that the temporary cavity (captured in "full recoil") is biggest about 1" from the front, and slowly tapers as it goes deeper in. If the bullet were still expanding, it would be the opposite shape. Despite Remington's claims of "controlled energy transfer," the shape of the temporary cavity is 100% typical of handgun hollowpoints. Golden Sabers are excellent performers from the expansion and penetration data I've seen, though.

    Rifles are a slightly different story, but I'd estimate that the longest distance most softpoints could continue to expand isn't much more than 6".

    Jacket shedding is actually evidence that the core doesn't continue to expand, if you think about it. If the core were still expanding (barring overexpansion), it would be wedging itself tightly against the inside of the jacket, preventing it from going anywhere. But if the core reaches its final shape within a few inches, there's less tension holding the jacket on, and it could slowly start to get pulled off by drag, then come off somewhere closer to the end.
     
  9. lbmii

    lbmii Member

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    Ok I took your data and sorted it by wound volume I also added a column for momentum. I then created a graph using the wound volume as the X axis and Energy as one Y axis and Momentum as another Y axis. It seems that momentum has a little straighter line with a R2 of 0.15 compared to the R2 of the energy line of 0.03. Of course both R2 are really bad.

    [​IMG]
     
  10. lbmii

    lbmii Member

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    I then eliminated all rounds 32 caliber and less and removed the 45 Schofield and the 30 carbine data. The lines straightened out a bit with the Momentum R2 now at 0.46 and the Energy R2 at 0.22. I noticed some odd rounds and pointed them out. One was a hot 45 Colt round and another was a 44 mag round that had much more Energy and Momentum for their wound volumes. The other was a 380 round that had a lot of wound volume for it’s fairly small energy and momentum.

    [​IMG]
     
  11. lbmii

    lbmii Member

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    Here is just the 40 S&W, note that the lines are very flat showing little to no gain in wound volume in relation to energy or momentum.

    [​IMG]
     
  12. lbmii

    lbmii Member

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    Here is just the 38 Special.

    Note that the Momentum and Energy lines have only a slight upward trend.

    There is only a slight relationship between wound volume relative to momentum and energy.

    [​IMG]
     
  13. lbmii

    lbmii Member

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    I went back to the graph with all of the data and changed the trendlines from starting at zero and let the computer do the calculations for the starting point. This greatly improved the R2 values. The momentum line still has a much better R2 value over the energy line.

    Note: The R2 shows how close points fall along a line. The best and maximum R2 you can have is 1.0 the lower your R2 is from 1.0 the less your points fall close to a straight line.

    [​IMG]



    Within the limitations of our data and within the limitations of the way in which we are calculating wound volume we can conclude:

    In all of the above graphs the momentum lines had a steaper slope and a higher R2 value than the energy lines. This shows a better relationship between momentum to wound volume than energy to wound volume.

    However the R2 values are all quite low so momentum and energy play a role in wound volume but there are other significant factors that are involved as well.
     
  14. coylh

    coylh Member

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    I did up another bullet type, this time .45 ACP Silvertips. There weren't as many examples as with the Gold dots.

    Bullet type Weight (grains) Velocity (feet per second) Penetration (inches) Final diameter (inches) Energy (foot-pounds) Hole volume (cubic inches) Source of data
    .45 silvertip 225 920 19.5 0.66 422.7903631 6.67132908 Street Stoppers
    .45 silvertip 185 1000 12 0.79 410.7131757 5.882003925 Street Stoppers
    .45 silvertip 185 951 10.7 0.78 371.4494068 5.112847796 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    .45 silvertip 185 899 9.6 0.75 331.9387993 4.241150082 http://www.firearmstactical.com/test_data/45acp/win45-185st-g30.htm
    .45 silvertip 185 940 9.75 0.85 362.906162 5.532639187 http://home.snafu.de/l.moeller/Zielwirkung/Frog.html
     

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  15. coylh

    coylh Member

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    And the 9mm/.357 silvertips...

    Bullet type Weight (grains) Velocity (feet per second) Penetration (inches) Final diameter (inches) Energy (foot-pounds) Hole volume (cubic inches) Source of data
    .380 silvertip 85 954 7.9 0.58 171.7443988 2.087242743 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    .357 silvertip 145 1166 15.8 0.58 437.6551164 4.174485486 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    9mm silvertip 147 902 14.6 0.53 265.5200472 3.221027824 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    9mm silvertip 115 1091 10.1 0.63 303.888488 3.148417764 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    .38 silvertip 125 842 10.15 0.53 196.7438215 2.239276193 http://www.firearmstactical.com/ammo_data/38special.htm
     

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  16. Zak Smith

    Zak Smith Moderator Emeritus

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    You should review the commentary on my FBI-PISTOL page. In particular, the observations. Momentum likely has a better relationship to wound volume because massier slower bullets rely less on "finicky" expansion mechanisms vs. the lighter and faster bullets, which are generally more easily defeated by getting clogged up.
     
  17. Cosmoline

    Cosmoline Member

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    I don't think any of this highlights inherent problems with the .308 so much as inherent problems with the Hague Convention. We force our cartridges to fight with both hands tied behind their backs, so to speak. Feed that M-14 with Barnes-X handloads and I can guarantee no bad guy will ever get up again--unless he can run around with his innards gone. But that's a different thread.
     
  18. coylh

    coylh Member

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    Oops. Forgot to add Street Stopper data:

    Bullet type Weight (grains) Velocity (feet per second) Penetration (inches) Final diameter (inches) Energy (foot-pounds) Hole volume (cubic inches) Source of data
    .380 silvertip 85 954 7.9 0.58 171.7443988 2.087242743 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    .357 silvertip 145 1166 15.8 0.58 437.6551164 4.174485486 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    9mm silvertip 147 902 14.6 0.53 265.5200472 3.221027824 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    9mm silvertip 115 1091 10.1 0.63 303.888488 3.148417764 http://apollo.demigod.org/~zak/firearms/fbi-pistol.php
    .38 silvertip 125 842 10.15 0.53 196.7438215 2.239276193 http://www.firearmstactical.com/ammo_data/38special.htm
    .357 silvertip 145 1290 14.3 0.65 535.690975 4.745179354 Street Stoppers
    .38 silvertip 110 995 8.6 0.67 241.771861 3.032061026 Street Stoppers
    9mm silvertip 115 1225 8 0.72 383.121853 3.257203263 Street Stoppers
    .380 silvertip 85 1000 6.5 0.63 188.7060537 2.026209452 Street Stoppers
     

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  19. RyanM

    RyanM Member

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    Really? It's always been my observation that bullets with small, narrow hollowpoint cavities are the most resistant to being clogged with fabric, since they don't get clogged in the first place.
     
  20. Zak Smith

    Zak Smith Moderator Emeritus

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    I didn't say anything about small vs. large cavities per se. In my data list, look at the "clothed" vs "bare" gel results for the heavier vs. lighter & faster bullets in a given caliber.
     
  21. Cosmoline

    Cosmoline Member

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    Great thread BTW. It's got me thinking a whole lot more about momentum. It's a factor which appears to play a very significant role, yet while I see ft. lbs. and velocity listed all the time I don't ever recall seeing the momentum of cartridge rounds listed anywhere.
     
  22. coylh

    coylh Member

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    Here are FMJ loads, for those stuck with them. Most of these are from Street Stoppers, since more people don't waste gelatin with fmj.

    Bullet type Weight (grains) Velocity (feet per second) Penetration (inches) Final diameter (inches) Energy (foot-pounds) Hole volume (cubic inches) Source of data
    .40 fmj 180 950 25 0.4 360.6505697 3.141592654 Street Stoppers
    .40 fmj 155 1125 22 0.4 435.5155338 2.764601535 Street Stoppers
    .45 fmj 230 835 27 0.45 356.0145059 4.294164458 Street Stoppers
    .45 fmj 185 1046 24.5 0.45 449.3678569 3.896556638 Street Stoppers
    9mm fmj 115 1155 24.5 0.36 340.5875085 2.493796248 Street Stoppers
    .380 fmj 95 955 17 0.36 192.3522432 1.730389234 Street Stoppers
    .32 fmj 71 905 18.5 0.32 129.098862 1.487858281 Street Stoppers
    .25 fmj 50 710 18 0.25 55.9568951 0.883572934 Street Stoppers
    9x18 109 1015 21.9 0.364 249.3018431 2.27896032 http://www.goldenloki.com/ammo/gel/9x18/gel9x18.htm
     

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  23. coylh

    coylh Member

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    Here is all of the major gelatin shoots from FirearmsTactical that I could find:

    Bullet type Caliber Weight (grains) Velocity (feet per second) Penetration (inches) Final diameter (inches) Energy (foot-pounds) Hole volume (cubic inches) Source of data
    SXT 9 95 865 7.6 0.59 157.8057149 2.077817965 http://www.firearmstactical.com/test_data/380acp/win380-95ssxt-b85.htm
    Silvertip 8.1 60 813 7.1 0.43 88.04389525 1.031062855 http://www.firearmstactical.com/test_data/32acp/win32-60st-b3032.htm
    Nyclad 9 125 752 7.4 0.65 156.9323944 2.455547358 http://www.firearmstactical.com/test_data/38spl/fed38spl-125nhp-swm60.htm
    SXT 10 180 905 11.2 0.7 327.2928896 4.310265121 http://www.firearmstactical.com/test_data/40sw/win40-180rsxt-g27.htm
    Win Expand Point 6.35 45 760 6.5 0.39 57.70409115 0.776483894 http://www.firearmstactical.com/test_data/25acp/win25-45xp-b20.htm
    LHP 5.58 30 1266 7.4 0.38 106.746974 0.839245061 http://www.firearmstactical.com/test_data/22lr/agu22-30smhv-r2245.htm
    Hydrashok 11.45 230 815 12.9 0.66 339.1641654 4.413340776 http://www.firearmstactical.com/tacticalbriefs/volume4/number1/article415.htm
    Hydrashok 11.45 165 915 9.5 0.68 306.685356 3.450097052 http://www.firearmstactical.com/test_data/45acp/fed45-165pdhs-g30.htm
    XTP 9 90 1010 11.2 0.45 203.8225186 1.781283035 http://www.firearmstactical.com/test_data/380acp/hor380-90xtp-b85.htm
    Golden Saber 10 165 1043 12 0.68 398.4918723 4.358017329 http://www.firearmstactical.com/test_data/40sw/rem40-165gs-g27.htm
    Gold Dot 9 124 1189 11.8 0.75 389.1816018 5.21308031 http://www.firearmstactical.com/test_data/9mm/geo9-124+p-g26.htm
    Silvertip 11.45 185 899 9.6 0.75 331.9387993 4.241150082 http://www.firearmstactical.com/test_data/45acp/win45-185st-g30.htm
    Tactical Grade 10 165 1027 12.5 0.65 386.3596271 4.14788405 http://www.firearmstactical.com/test_data/40sw/pro40-165-g27.htm
     

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  24. Ivy Mike

    Ivy Mike Member

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    Correct me if I'm wrong, but here is what I got from the data and discussion.

    Energy of a round is its ability to penetrate and expand a bullet.

    Energy is best distributed over the entire length of its stay in a body instead of dumping it at the last minute.

    Ideally, the bullet would enter the body, expand violently and continue to the "ideal" depth.

    In the real world, the bullet enters and expands while moving to its final depth. Energy is simply the bullets ability to accomplish this and has little "direct" effect on wounding.
     
  25. coylh

    coylh Member

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    Ideally the bullet would penetrate half the depth of the target and detonate. ;)

    But we're stuck with lead pellets.
     
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