Quantcast
  1. THR Just moved.  See problems?  Make sure you're logged in and come to this thread and tell us about it!

    Dismiss Notice

Statistical Analysis of "Energy Transfer"

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

Thread Status:
Not open for further replies.
  1. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    Analysis was conducted by looking up gelatin data on various cartridges. A total of 422 shooting results were analyzed and plotted. Analysis was primarily based on Energy and Wounding Potential.

    Energy in foot-pounds was calculated by the following formula:

    1/2 * (M/7000/32.174) * V^2
    Where M is bullet mass in grains, and V is bullet velocity in feet per second

    The Wounding Potential in cubic inches of a given bullet was calculated by another formula:

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

    Energy was plotted as the abscissa, and Wounding Potential as the ordinate (X and Y axes, in layman's terms), producing this graph:
    [​IMG]

    While it appears at first glance that there is some correlation between Energy and Wounding Potential, further analysis reveals that this is not the case.

    When all "mousegun" calibers (.22 LR, .25 ACP, .32 ACP, and .32 NAA) are graphed together, there is still some correlation:
    [​IMG]

    However, if all 9mm calibers (.38 SPL, .357 Magnum, 9x17mm Short, 9x18mm Makarov, and 9x19mm Parabellum) are plotted, the result is:
    [​IMG]

    If all 10mm calibers (.40 S&W and 10mm Auto) are plotted together:

    [​IMG]

    And if all 11mm to 12mm calibers (.44 SPL, .44 Magnum, .45 ACP, .45 Colt, .45 GAP, .45 Schofield, and .45 Super) are plotted:
    [​IMG]

    Sources of test data:

    http://www.firearmstactical.com/wound.htm
    http://www.goldenloki.com/ammo/gel/tests.htm
    http://www.stevespages.com/page8f.htm (penetration depths divided by 1.5, as this is the approximate ratio between water penetration and gelatin penetration)
    http://www.handgunsmag.com/ammunition/


    2 more graphs in next post (limited to 5 attachments).
     

    Attached Files:

  2. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    Lest anyone claim that all cartridges of a certain diameter were lumped together for the sake of reducing correlation, here are two additional graphs.

    One on which is plotted only 9x19mm results:
    [​IMG]

    And one on which only .45 ACP is plotted.
    [​IMG]

    It's worth noting that Cor-Bon cartridges consistently did very poorly, despite their high energy levels. If you see a dot further to the right and lower than the rest, odds are that's a Cor-Bon.

    From these results, the logical conclusion is that maximum damage is inflicted by the best designed bullets, when they are driven at their optimum velocity window. If poor bullets are used, or good bullets are shot at velocities for which they are not designed, results suffer.
     

    Attached Files:

  3. KONY

    KONY Member

    Joined:
    Aug 30, 2004
    Messages:
    1,161
    Location:
    Fairfax, Northern Virginia
    RyanM,

    Nice plots! Here's my take on this data:

    First one suggest a moderate to high correlation across all calibers.

    Second one does as well but has far fewer data points (understandable as small calibers are used less for defense).

    The rest of the plots suggest that the correlations are very low/ near zero ("orthogonal" shape or no relationship) between energy & wounding ability across these "defense" loads. Bulls**t, you say? Well, maybe not. These findings can be explained by the lack of accounting for a third variable(s) which would moderate these bivariate correlations. Post hoc, I would say that one of these variables would be "shot placement" as defense calibers (especially 9mm) have reputations of over-penetration. Moral of the story? Caliber/ stopping power is not EVERYTHING. You need to account for other variables (like "shot placement", etc.)

    Hope this made sense! ;)
     
  4. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    Shot placement is definitely a huge factor when shooting humans.

    The plots are based solely on gelatin and water results, though; a rough estimate of just how big a hole a given bullet can make, and that's pretty much it.

    Most "energy transfer" advocates claim that more energy translates to a greater amount of tissue destruction regardless of placement (for instance, that if a 250 ft-lb bullet destroys 1 ounce of tissue, a 500 ft-lb bullet should destroy 2 ounces), and the plots were made for the sake of proving or disproving that assertation.

    The real correlation seems to be between caliber and damage. Bigger caliber means bigger hole. That correlates with energy somewhat because a wider barrel provides greater volume for powder combustion, and thus greater velocity imparted on the bullet (which translates to energy); similarly, a wider cartridge case holds more powder, and allows yet more velocity.

    Like a 9mm +P, at 38,500 PSI, might be able to shoot a 124 grain bullet at 1300 fps through a 5" barrel. A .460 Rowland, on the other hand, is 40,000 PSI, and can launch a 200 grain bullet at something like 1450 fps, through the same length barrel. Same sectional density bullet, same barrel length, but the extra powder and barrel volume give the .460 enormously more power.
     
  5. KONY

    KONY Member

    Joined:
    Aug 30, 2004
    Messages:
    1,161
    Location:
    Fairfax, Northern Virginia
    Ahhh, good point! Thanks for clearing that up. :cool:
     
  6. JohnKSa

    JohnKSa Moderator Staff Member

    Joined:
    Jan 1, 2003
    Messages:
    13,913
    Location:
    DFW Area
    Looking at the overall plot (everything), I see a couple of things.

    It would probably be more helpful if you grouped the plots by bullet type. It looks to me like the FMJ/nonexpanding and the frangible ammo is decorrelating the graph.

    Ok there's another thing-- Most SD ammo is designed to expand and penetrate to a specific depth--since that design depth is considered "ideal" more or less all SD ammo (with the exception of the frangibles) is designed to penetrate to about the same depth. That means that once some energy threshold is reached (the point at which it is possible to get the "ideal" amount of penetration and still have an expanding bullet)the trend goes away. In other words, after some threshold energy level is reached or passed, things tend to equal out...

    The lower energy calibers can't make the "ideal" depth with expanding ammunition and so their numbers suffer.
     
  7. Mulliga

    Mulliga Member

    Joined:
    Jan 13, 2004
    Messages:
    2,251
    Location:
    Gainesville, Florida
    As I said in the other thread, does that mean you would take a 1911 over a Garand in a gunfight at 15 yards?
     
  8. R.H. Lee

    R.H. Lee Member

    Joined:
    Jan 26, 2004
    Messages:
    7,376
    Location:
    CA
    I don't know that 'energy transfer' is a significant factor with handgun bullets. You want tissue damage and severed blood vessels. An exit wound also helps lethality, and it makes another hole for the SOB to bleed out and hopefully creates a deadly pneumothorax effect.
     
  9. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    JohnKSa, I would have done that if FMJs had been a substantial portion of the rounds plotted. Such as it was, almost half the .32 caliber and under rounds were FMJ's (15 out of 39), but above .32, a grand total of 4 FMJs were plotted. In all calibers, zero frangibles were plotted except for a single RCBD which failed to fragment and performed like a regular JSP instead.

    Penetration figures were as follows:

    Gawd-awful (<6"): 2
    Inadequate (6-<9"): 47
    Marginal (9"-<12"): 116
    Optimal (12"-18"): 220
    Satisfactory (>18"): 23

    Which only adds up to 408, so I must have skipped a few digits. Still, most of the rounds ended up in the FBI's "optimal" category.

    Of course, the inadequate-to-marginal mark is "optimal" for some schools of thought.

    I might be able to do some energy vs. wounding ability plots based on penetration category tomorrow.
     
  10. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    Depends on the ammo. .45 hardball against .30-06 FMJ, and .45 probably makes a bigger hole at that range. My analysis is based on handgun calibers only, though. This is the handgun forum, after all. Rifles are a whole nother ballgame, since most rifle caliber softpoints are capable of damaging tissue beyond what the bullet (and its fragments, if any) directly contacts, unlike handgun rounds.

    In the same general category, though, I'd take a .45-70 over a Garand, or a 12 gauge over either. More meaningful discussions usually involve comparing apples to pears and oranges to grapefruits instead of apples to oranges, yaknow?
     
  11. JohnKSa

    JohnKSa Moderator Staff Member

    Joined:
    Jan 1, 2003
    Messages:
    13,913
    Location:
    DFW Area
    Not terribly surprising--that's what they're designed to do.

    Under 300ft/lbs there's a pretty clear linear relationship. It looks like somewhere around 300ft/lbs something happens and the linear trend goes away.

    I think that's the point at which ammo manufacturers can assure reliable expansion while still achieving "optimal" penetration. It would seem that after that point, adding more energy doesn't significantly improve the wound channel size since the ammo manufacturers limit penetration by controlling expansion.

    The key is that there's not much difference in the size of expanded bullets when you're talking about decent quality ammo. And if the ammo makers are holding the penetration down, that should mean after you reach around 300ft/lbs, the wound channel sizes will stay pretty constant in size.

    Ok, here's a thought. Plot caliber vs wound channel. I'll bet the plot looks almost identical.
     
  12. Zak Smith

    Zak Smith Moderator Emeritus

    Joined:
    Dec 24, 2002
    Messages:
    9,043
    Location:
    Fort Collins, CO, USA.
    http://www.firearmstactical.com/hwfe.htm
    Handgun Wounding Factors and Effectiveness

    Special Agent UREY W. PATRICK

    FIREARMS TRAINING UNIT
    FBI ACADEMY
    QUANTICO, VIRGINIA

     
  13. Mulliga

    Mulliga Member

    Joined:
    Jan 13, 2004
    Messages:
    2,251
    Location:
    Gainesville, Florida
    .45 hardball against .30-06 FMJ.

    I don't see what's so fundamentally different. They are both projectiles, and both will not expand.

    The .30 bullet will be significantly smaller, but with significantly more energy. People always say handgun bullets are a poor choice for stopping human beings, but if that's true, that would mean a rifle in a non-softpoint/hollowpoint design would be worse at wounding than a handgun of larger caliber (and maybe that is so).

    I'm not an expert on any of this. :) My question is: how tough is it for a bullet to go through bones? If a .45 ACP bullet hit a rib or a humerus, does it keep right on going toward the vital organs/spinal column? Does it have enough steam left to destroy vertebrae?
     
  14. OF

    OF Member

    Joined:
    Dec 26, 2002
    Messages:
    2,988
    Very cool data, Ryan. Thanks for taking the time to do that.

    - Gabe
     
  15. Sean Smith

    Sean Smith Member

    Joined:
    Dec 28, 2002
    Messages:
    4,925
    No, because the wounding mechanisms aren't quite the same. Projectiles moving at 2,000-3,000 ft/sec produce very different effects on target from projectiles moving at 900 ft/sec. At 900 ft/sec, a short, fat pistol bullet basically just pokes a hole. A long, skinny rifle bullet moving 3,000 ft/sec will often split, fragment, tumble, and/or corkscrew though the target. Furthermore, at 2,000+ ft/sec, hydrostatic shock becomes a very real wounding mechanism, which is not the case with pistol bullets... they just go too slow.

    People saying kinetic energy doesn't matter are sort of right, but sort of full of crap.

    A projectile damaging a target is doing work on the target, i.e. it applies a force that causes a displacement. Energy is the capacity to do that work, and kinetic energy is the energy derived from motion. See where this is going? All else being equal, a projectile with more kinetic energy always has a greater potential to damage a target.

    On the other hand, only talking about kinetic energy is a gross oversimplification. It ignores too many other factors to produce a real-world answer. Depending on the target, and the bullet design, bullets can: expand, tumble, fragment, flatten, go sideways, make a clean hole, or even bounce off the target.

    More energy just means the bullet could POTENTIALLY do more work, it doens't mean that it will actually do the work you need it to do. For instance: it could blow right through the target, barely slow down, and hardly harm the target at all. Or fragment so violently in such a short distance that nothing vital gets damaged.

    Oh, and having studied statistics, none of those graphs show any correlation to speak of... they are either (a) beyond weak, or (b) nil.
     
  16. KONY

    KONY Member

    Joined:
    Aug 30, 2004
    Messages:
    1,161
    Location:
    Fairfax, Northern Virginia
    Agreed! :cool:
     
  17. griz

    griz Member

    Joined:
    Dec 25, 2002
    Messages:
    2,371
    Location:
    Eastern Virginia
    Interesting but I'm not sure the formula for hole size is valid. It ignores any damage the bullet would do past its own diameter, however much that might be. And it assumes that the bullet will expand virtually instantly to its final diameter and stay that way. Some bullets achive penetration by expanding slowly and so would be scored higher. Some may expand quckly but lose diameter at the very end buy fragmenting or further expansion, which would hurt their score.

    If there was a way to measure the actual volume of the gelitan wound I would like to see what that showed. Thanks for the information though. I'm probably being overly critical of it.
     
  18. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    '

    Despite having more energy, a .30-06 FMJ will barely do diddly.
    http://www.firearmstactical.com/images/Wound Profiles/M80.jpg
    That's .308 ball, but there's very little difference between .30-06 and .308. And .308 ball is notorious for failing to stop people. If you read Blackhawk Down, I think there's one instance where a little old man was able to absorb 3 or 4 bursts from an M-60 before deciding to sit down for awhile.

    In that one instance, the round "tumbled" after 6" penetration, but in practice FMJ rifle bullet "tumbling" is almost completely random. I believe a test of .223 ball (which has a steel tip and is extremely long, so it's even less stable than .30 caliber bullets) had an average "tumble" depth of 3", but an extreme spread of 1" to 12", depending on all kinds of factors. So basically, all you're guaranteed with .30 caliber ball is a .30 caliber or smaller hole, with maybe a slit-shaped hole near the end, that's basically like a knife wound.

    But softpoints are a completely different proposition. http://www.firearmstactical.com/images/Wound Profiles/308 Winchester.jpg
    Ouch. :eek:
     
  19. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    I agree with you there, though you're using the goofy "hydrostatic shock" term to describe temporary cavitation (hydro = water, static = nonmoving, shock = a violent and sudden motion, hydrostatic shock = water that moves while standing still; in the correct usage of the word, hydrostatic pressure testing of scuba tanks involves pressurizing water which does, indeed, remain still, unless the tank fails). That's why my graph only has pistol bullets on there (though I think one .30 carbine might have slipped in).

    And I think you're confusing .223 ball for... every other type of rifle FMJ. Most rifle FMJs will "tumble" once or twice after several inches of penetration, but all that results in is a narrow, slit-like wound, like a knife stab wound. Some FMJs do indeed fragment, like .223, Mark something .303, and steel-jacketed 7.62x51mm (American made 7.62mm doesn't do that, though), but the majority don't.

    In reality, temporary cavitation damages tissue only if the force is substantial enough to exceed the tensile strength of tissue; something like 150 to 500 PSI (in comparison, water has a tensile strength of zero PSI, which is why a powerful bullet can blow up a water jug). Below that pressure, all temporary cavitation can do is cause bruising due to blunt trauma. Bullets which fragment will weaken tissue and allow force to be concentrated on the weakened area, but pistol bullets generally do not produce enough force to cause a very large amount of tearing.

    You are totally misunderstanding exactly what kinetic energy is. While energy is the ability to do work, the amount of work done is never equal to the amount of energy put into a system. You're also confusing momentum, force, and energy. The three are not interchangable in this universe. And if they are, then I am going to personally bring Isaac Newton and Albert Einstein back from the grave, slap the crap out of them, and demand that they write up some new equations which describe this energy-momentum-force phenomenon.

    Look at it this way. If a 1 pound object hits another 1 pound object at 1 fps, and they stick together and keep moving, the velocity of the resulting 2 pound mass will be 1/2 fps. Starting energy of 0.0155 ft-lbs, final energy 0.00777 ft-lbs. Starting momentum of 0.0311 lb*ft/s, final momentum of 0.0311 lb*ft/s. Force exerted by the first object is .0155 pounds (1/2 poundal). Simple, high school level physics.

    Momentum is conserved as movement; kinetic energy is not conserved as movement. So what happened to the "missing" energy? Simplest terms I can put it in is that the universe stole it. Darn universe. The only energy which is used to actually move things around on the macro scale is the energy which tags along with the momentum; the rest of the energy is converted into heat, vibration, noise, etc.
     
  20. MrAcheson

    MrAcheson Member

    Joined:
    Dec 26, 2002
    Messages:
    1,629
    Location:
    Newark, DE and APG, MD
    A few comments.

    1) You should not have altered the axes on the graphs when you broke the points down by caliber. (Or maybe excel did this by autoscaling them.) The overall and caliber graphs should be on the same axes so you can compare directly between them. The overall graph looks plausible but the individual calibers are just clouds. But they aren't just clouds. They are clouds at given locations on the overall graph and automatically scaling the axis skews the picture.

    2) Use colors to indicate feature on the graphs. Plot the 9mm in one color, the .44/.45 in another etc etc. When you break down to specific calibers, try plotting the manufacturers (or bullet weights) in given colors. This might show some useful trends and will allow you to put more information on a graph.

    3) I'm also with Griz. Your wound volume equation is a lowest bound estimate which applies certain assumptions. It is going to favor heavier bullets with lower energies for a given caliber because they penetrate more deeply and expand to roughly the same size. However it will neglect any damage outside of the bullet radius. A more informative number would be taken directly from the gelatin testing. But the likelihood that you have a wound volume number from testing that is comparable across testers is probably unlikely. So you went with what you got.

    Overall though good work. Very interesting.
     
  21. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    That's why pistol bullets were the only ones plotted. If you look at that one link for a .308 softpoint, rifle bullets can do truly massive amounts of damage, since the force they exert radially outwards exceeds the tensile strength of tissue.

    As a general rule, however, pistol bullets do not exert enough force to tear tissue to any degree; even ultra high-energy fragmenting rounds like a Glaser. http://www.firearmstactical.com/images/Wound Profiles/357 Magnum Glaser.jpg

    In fact, most pistol rounds don't even exert enough force to crush tissue with their entire width; a bullet that expands to .75" may very well only make a hole that's .5" wide or smaller. How efficient a bullet of X width is at making a hole is pretty hard to determine, though, so I just graphed the "theoretical maximum," using the expanded diameter. In actual practice, holes created will be much smaller than what's on the chart.

    Gelatin hole size doesn't really correlate with tissue that well, so plotting that would be pretty meaningless. The only thing gelatin models is the penetration depth and temporary cavity diameter of penetrating projectiles shot into living, anesthetized, swine thigh and buttock tissue. Gelatin's tensile strength is so low, however, that even pistol bullets are able to tear it to a fairly significant degree beyond the diameter of the bullet. These tears have been correlated with temporary cavitation width in living, anesthetized swine or dog thigh muscle tissue, through the use of high-speed photography, I believe.

    In other words, if X bullet makes 3" wide tears in gelatin, then X bullet shot into a pig's butt will stretch the muscle tissue out 3" for a fraction of a second, then the muscle will bounce back and the remaining hole will be, at most, the diameter of the bullet, and probably smaller.

    Eewww, don't try visualizing that. :D
     
  22. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    MrAcheson,

    1 & 2; I really would have liked to do different colors and kept scales, but I don't even have Excell. All I have is Microsoft Works Spreadsheet, which absolutely sucks. Can't change colors, it autoscales no matter what, etc. I also used to have a regression analyzer, but my trial period ran out, so I have to shell out $30 if I want to keep playing with it.

    3; see other replies for explanations. While no pistol bullet (barring .454 casull, .500 S&W mag, and other rounds which were excluded from the plots anyway) can really do significant damage beyond what the bullet itself directly contacts, I do agree that higher velocity bullets will do a bit more damage than low velocity ones, given the same expanded diameter; I (and my physics professors, I should add) firmly believe that this is due to the difference in force exerted by the bullet, rather than the difference in energy, however. It would've been nice if I could account for that difference, but there's no "hard and fast" way of calculating just how big a hole a given bullet will make (and believe me, I've tried). A general rule of thumb, though, seems to be that doubling velocity doubles the efficiency in crushing a hole (if a .8" bullet makes a .3" hole at 800 fps, then the same bullet with the same shape at 1600 fps will make about a .6" hole; but you have to know that it makes a .3" hole at 800 fps from some other source first, and it only applies for that one bullet with exactly that shape).
     
  23. Sean Smith

    Sean Smith Member

    Joined:
    Dec 28, 2002
    Messages:
    4,925
    Semantic masturbation. It is a pretty widely accepted term with a well-understood meaning.

    http://en.wikipedia.org/wiki/Hydrostatic_shock

    ... Which is EXACTLY what I said.

    Quoting myself:

    Potential != actual.

    No. My statements are based on common textbook definitions of energy and work. And I didn't even mention momentum last I checked.

    Straw man. I never said they were interchangeable. My statements, if you actually read them, don't suggest that they are. Quoting myself:

    Last I checked, this wasn't open to dispute.

    How is this statement not accurate? Are you appealing to magic or something? Note the colossal caveat ALL ELSE BEING EQUAL. Note the use of the rather conditional term POTENTIAL. It is there for a reason. ;)

    By the way, what are your correlation coefficients?
     
  24. RyanM

    RyanM Member

    Joined:
    Jan 4, 2005
    Messages:
    4,412
    Location:
    PA
    I'm just tired of people saying that energy = ability to do work, therefore energy = damage, so I typed up a version of my "standard reply."

    It's like saying that entropy increase = spontaneuity, therefore things do not burn well at high temperatures, and burn great at freezing temperatures. Gross oversimplification with no real basis in fact.


    But I need to read stuff more carefully instead of skimming, mostly. You're right that more energy can result in the potential to do more damage. But that's because more energy means more mass (bigger size, potentially more penetration, more material for expansion, etc) and/or more velocity (more ability to expand, potentially more penetration, etc).

    There's nothing about energy that makes it a good indicator of performance, unless every single bullet tested is designed to give optimal results for that particular weight/velocity combination. Sure, energy plays a part, but accounting for mass, velocity, and design seperately gives much better results than just looking at energy, which you've already more or less stated; that's all I was trying to prove by making scatter plots.

    It's kinda funny that you linked to an article that I edited somewhat, though (mostly clarification of exactly what temporary cavitation can and cannot do, exactly like I've done in posts here). You should check out http://en.wikipedia.org/wiki/Stopping_power , which I wrote the very first draft of, and have been editing and adding to since.

    Oh, correlation coefficient... I have no idea. Microsoft Works Spreadsheet is really crappy. Just by eyeballing the plots, I'd say correlation is about nil, when similar caliber bullets are analyzed. Some correlation when all results are plotted together, but that appears to be because smaller caliber handguns usually throw lighter bullets at lesser velocities, thus giving lower energy figures.
     
  25. MrAcheson

    MrAcheson Member

    Joined:
    Dec 26, 2002
    Messages:
    1,629
    Location:
    Newark, DE and APG, MD
    Roughly, very roughly, energy equals ability to do damage. Your overall chart shows that pretty well. The problem is that, as your individual charts show, it is a very noisy number and is not something to be completely relied upon. It is a very very gross estimator of actual performance.

    The reason is that how the energy is used matters. It could go into tearing flesh and breaking bone. It could go into heat. Energy as a number doesn't tell you that. If all that energy turns into heat, it might be enough to raise the temperature of your coffee a degree or so. It really isn't that much.

    You can't say correlation is nil when you are comparing way too many variables. Even with the same cartridge you are probably comparing different muzzle velocities and bullet weights. Of course correlation will suck then. There is a good chance that those individual calibers have a lot of bandedness and order to them that you aren't capturing.

    I may have an old copy of Excel lying around at home. I'll check. If not try one of the freeware office suites like OpenOffice. I prefer the MS stuff just because everyone seems to have it, but it might be better than what you have.
     
Thread Status:
Not open for further replies.
  1. This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
    By continuing to use this site, you are consenting to our use of cookies.
    Dismiss Notice