[RyanM]

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:
http://www.thehighroad.org/attachment.php?attachmentid=23184&stc=1

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:
http://www.thehighroad.org/attachment.php?attachmentid=23183&stc=1

However, if all 9mm calibers (.38 SPL, .357 Magnum, 9x17mm Short, 9x18mm Makarov, and 9x19mm Parabellum) are plotted, the result is:
http://www.thehighroad.org/attachment.php?attachmentid=23179&stc=1

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

http://www.thehighroad.org/attachment.php?attachmentid=23180&stc=1

And if all 11mm to 12mm calibers (.44 SPL, .44 Magnum, .45 ACP, .45 Colt, .45 GAP, .45 Schofield, and .45 Super) are plotted:
http://www.thehighroad.org/attachment.php?attachmentid=23181&stc=1

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).

[RyanM]

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:
http://www.thehighroad.org/attachment.php?attachmentid=23185&stc=1

And one on which only .45 ACP is plotted.
http://www.thehighroad.org/attachment.php?attachmentid=23186&stc=1

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.

[KONY]

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! ;)

[RyanM]

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.

[KONY]

Ahhh, good point! Thanks for clearing that up. :cool:

[JohnKSa]

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.

[Mulliga]

The real correlation seems to be between caliber and damage. Bigger caliber means bigger hole.

As I said in the other thread, does that mean you would take a 1911 over a Garand in a gunfight at 15 yards?

[R.H. Lee]

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.

[RyanM]

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.

[RyanM]

As I said in the other thread, does that mean you would take a 1911 over a Garand in a gunfight at 15 yards?

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?

[JohnKSa]

most of the rounds ended up in the FBI's "optimal" category.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.

[Zak Smith]

http://www.firearmstactical.com/hwfe.htm
Handgun Wounding Factors and Effectiveness

Special Agent UREY W. PATRICK

FIREARMS TRAINING UNIT
FBI ACADEMY
QUANTICO, VIRGINIA


Conclusions

Physiologically, no caliber or bullet is certain to incapacitate any individual unless the brain is hit. Psychologically, some individuals can be incapacitated by minor or small caliber wounds. Those individuals who are stimulated by fear, adrenaline, drugs, alcohol, and/or sheer will and survival determination may not be incapacitated even if mortally wounded.

The will to survive and to fight despite horrific damage to the body is commonplace on the battlefield, and on the street. Barring a hit to the brain, the only way to force incapacitation is to cause sufficient blood loss that the subject can no longer function, and that takes time. Even if the heart is instantly destroyed, there is sufficient oxygen in the brain to support full and complete voluntary action for 10-15 seconds.

Kinetic energy does not wound. Temporary cavity does not wound. The much discussed "shock" of bullet impact is a fable and "knock down" power is a myth. The critical element is penetration. The bullet must pass through the large, blood bearing organs and be of sufficient diameter to promote rapid bleeding. Penetration less than 12 inches is too little, and, in the words of two of the participants in the 1987 Wound Ballistics Workshop, "too little penetration will get you killed." 42,43 Given desirable and reliable penetration, the only way to increase bullet effectiveness is to increase the severity of the wound by increasing the size of hole made by the bullet. Any bullet which will not penetrate through vital organs from less than optimal angles is not acceptable. Of those that will penetrate, the edge is always with the bigger bullet.44

[Mulliga]

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...

.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?

[OF]

Very cool data, Ryan. Thanks for taking the time to do that.

- Gabe

[Sean Smith]

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).

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.

[KONY]

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

Agreed! :cool:

[griz]

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.

[RyanM]

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?

Despite having more energy, a .30-06 FMJ will barely do diddly.
http://www.firearmstactical.com/images/Wound%20Profiles/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%20Profiles/308%20Winchester.jpg
Ouch. :eek:

[RyanM]

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.

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.

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.

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.

[MrAcheson]

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.

[RyanM]

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.

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%20Profiles/357%20Magnum%20Glaser.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.

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.

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

[RyanM]

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).

[Sean Smith]

though you're using the goofy "hydrostatic shock" term to describe temporary cavitation

Semantic masturbation. It is a pretty widely accepted term with a well-understood meaning.

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

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.

... Which is EXACTLY what I said.

Quoting myself:

More energy just means the bullet could POTENTIALLY do more work

Potential != actual.

You're also confusing momentum, force, and energy.

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

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.

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

Energy is the capacity to do that work, and kinetic energy is the energy derived from motion.

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

See where this is going? All else being equal, a projectile with more kinetic energy always has a greater potential to damage a target.

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?

[RyanM]

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.

[MrAcheson]

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.

[RyanM]

If you want to fiddle with the numbers and graphs yourself, attached is the spreadsheet with just the figures, and no graphs. Bullet descriptions are extremely vague, since it was already exhausting enough to type out all those darn numbers. If you want to try correlating them to the actual shots, data was put in in about the same order as the sources are listed.

And I really would say that correlation is close to nil, when you look at the results for plotting just rounds of a single caliber. If increasing energy really does increase wounding ability, shouldn't putting more energy on a 9x19mm (or other) bullet increase the performance? Shouldn't .357 magnum results consistently be above and to the right of 9mm parabellum? Plotting hasn't shown much of a difference, though.

Sure, more energy = more damage when comparing a .38 and a .44, but that type of comparison is pretty much the main reason for the total graph showing any correlation.

[Shane333]

I'm very interested in this. Right now I'm using a CZ83 (.380) with Rem. GoldenSaber 102 gr. bullets. I'd hoped the heavier .380 HP bullet would give me best balance of weight and expansion. However, if penetration is the single most important variable, I may do much better finding a hot loaded FMJ cartridge.

I'd love to see the data sorted by caliber.

[RyanM]

The majority of my .380 ACP data was from http://www.stevespages.com/page8f380acp.html

Since those shots were fired into water jugs, divide penetration depth by 1.5 for approximate penetration in gelatin. The IWBA's minimum penetration is 12.5" in gelatin (~19" in water), and the FBI's minimum is 12" (18" water). On there, Golden Saber only managed the equivalent of 9.33".

Penetration is really only the most important variable when comparing cartridges and guns that you already shoot well. Shot placement is probably the single most important factor, but inadequate penetration can negate shot placement.

The biggest single example I can think of, and the reason for the FBI's penetration requirement, is the 1986 Miami shootout. Early on in the gunfight (the first gunshot wound which Platt received, in fact), Special Agent Dove hit Platt in the right arm, just above the elbow, with a 9mm +P 115 grain Winchester Silvertip. The bullet severed Platt's brachial artery, cutting off all blood flow to Platt's right hand, and kept going into his chest, severing several large blood vessels in there; at autopsy, Platt's right lung was totally collapsed and nearly a quart and a half of blood was in his chest cavity. That bullet stopped one inch short of penetrating his heart.

Despite the severity of the wound (in fact, it was that wound which actually killed Platt; while Mireles was able to stop both Platt and Matix with spinal cord hits, Platt actually bled to death due to the bleeding from Dove's first hit), and the fact that his right arm was hit again by a shot which shattered his radius (forearm bone on the thumb side), almost totally disabling his right hand, Platt was able to shoot Special Agent McNeill in the neck, SA Grogan fatally in the chest, SA Dove twice in the head, and SA Hanlon in the groin.

If the bullets issued to those FBI agents had penetrated 2 or 3 inches more, Dove's shot would have struck Platt in the heart, and it's estimated that he would have bled out much sooner; a matter of inches could have saved two lives, a neck, and a groin. 9mm 115 grain +P Silvertips penetrate only around 9" in gelatin, thus the current FBI requirement is 12" to 18".

[JohnKSa]

If increasing energy really does increase wounding ability, shouldn't putting more energy on a 9x19mm (or other) bullet increase the performance?The numbers aren't designed to test that premise. There are many more variables than just bullet energy in those numbers.

One thing I keep saying that so far has been completely ignored is that wound channel size depends heavily on penetration and penetration is tightly controlled by ammo makers--at least in their premium SD loadings. That throws a big monkey wrench into the results here--you have ammunition designers intentionally limiting penetration and therefore wound channel size. Plotting these plots as if energy is the main variable totally ignores that fact.

That's what I was saying with my earlier post. You can see a clear linear trend up to about 300ft/lbs. My speculation is that 300ft/lbs is the point at which an ammo manufacturer can guarantee good expansion with "ideal" penetration. BEFORE that point, they're getting good expansion, but they can't get "ideal" penetration. So the wound channels are getting deeper and deeper as the energy goes up. At the 300ft/lb mark the linear trend goes away because everything's making ideal (or can easily be made to make ideal) penetration so then wound channel size starts to become more dependent on the ability of the ammo designer.

[MrAcheson]

I did a little work and sorted through the numbers by caliber.

http://www.thehighroad.org/attachment.php?attachmentid=23232&stc=1

The navy blue rounds are the mouseguns.

The yellow rounds are the low pressure .38/9mm calibers like the blowbacks and .38special.

The reds are the higher pressure 9mm rounds.

The lighter blue rounds are .40 and 10mm.

The greens are the .44specials and .45s.

The 2 blacks are .44mag and .30 carbine.

I'll do more work with this when I get a little free time.

[MrAcheson]

I looked at it a little more. The reason that 9mm is doing poorly is basically that there is an expansion ceiling it can't pass. The 9mm/.38s average around ~.55 inches. The .44/.45s average a much higher .71 inches. The penetration is similar (12 vs. 13) but the .45s frontal area is almost twice as much (.24 sq in vs. .40 sq in).

So we come back to whether this wound model is accurate or not.

[coylh]

Can I take a moment, and compliment all involved in this thread: it's better than 90% of the gun magazine articles I've read! This is facinating stuff!

[RyanM]

The reason that 9mm is doing poorly is basically that there is an expansion ceiling it can't pass.

Sounds about right to me. .355" to .55" is 1.55x expansion, while .451" to .71" 1.57x expansion. Bigger bullet = bigger hole, since I believe bullet size makes more of a difference than velocity. Not 100% certain, though.

Though if you want to, it's no huge task to graph for anything else you want. Let's see, surface area of a cylinder, and surface area of a cone...

Surface area of cylinder:
http://www.thehighroad.org/attachment.php?attachmentid=23247&stc=1

Surface area of cone:
http://www.thehighroad.org/attachment.php?attachmentid=23248&stc=1

And then because higher velocity bullets usually make a bigger hole for a given expanded diameter, volume of a cylinder * velocity:
http://www.thehighroad.org/attachment.php?attachmentid=23249&stc=1

Interesting, a much stronger correlation. Of course, the same variable (velocity) being used on both axes might be to blame. Still, let's see if the correlation holds up when seperating by calibers...

All 9mm (.355" to .364") calibers:
http://www.thehighroad.org/attachment.php?attachmentid=23250&stc=1

Correlation seems to be holding up.

But then when plotting 9x19mm alone:
http://www.thehighroad.org/attachment.php?attachmentid=23251&stc=1

Oops, falls apart again. Plotting any individual caliber like that results in even more chaotic results.

I'll leave it to the reader to determine if using the same variable on both axes is valid or not.

[RyanM]

.40 and 10mm graphed together produce pretty poopy results:
http://www.thehighroad.org/attachment.php?attachmentid=23252&stc=1

And graphing .44 and .45 (all) together isn't much better:
http://www.thehighroad.org/attachment.php?attachmentid=23253&stc=1

[coylh]

Ryan: I feel your pain. I searched for every 9mm Gold dot gelatin shooting I could get my hands on. I picked that one because it's my carry load. Then tried to figure out Excel's formulas. Please correct if I did anything wrong. ;)

I wanted to see what happens when the same bullet (as much as possible) is charted at different energy levels. I've included the spreadsheet in case anyone wants to see the data.

[RyanM]

Looks like better correlation on Gold Dots. But were the results all three weights (or more, if they make them), or predominantly 1 or 2? I spot a couple "fliers" above the main line, which I'd bet are 147 grain ones.

In the case of Gold Dots, it does seem like you can put as much velocity on them as you want, and still get darn good performance. Like that Doubletap .45 ACP (not super, amazingly) load, 1010 fps on a 230 grain bullet; .95" expansion and 15.25" penetration!

Makes me wonder why Cor-Bon doesn't use Gold Dots for their loadings; whatever brand bullet they're using do not hold up well at all at the high velocities.

[coylh]

The data has everything from 90-158 grain. I found a 180 grain result, but it didn't have expansion data unfortunately.

The three fliers are:
124 grain@1192, 12.2" .79
124 grain@1183, 11.1" .81
124 grain@1181, 11.6" .78

[Toejam]

RyanM,
Energy is always conserved. Energy is neither created nor destroyed. It only changes forms (assuming classic Newtonian physics). In your example, the Universe did not “steal” the “missing energy”. The “missing energy” was used to create a non-elastic collision.

There are two types of collisions, elastic and non-elastic. In elastic collisions (think billiard balls), kinetic energy and momentum are both conserved.

Your example is of a non-elastic collision. For a non-elastic collision to occur, some of the kinetic energy must be converted into thermal, chemical or potential energy two keep the two colliding bodies from bouncing off of one another.

For example...
When a bullet and a body have a non-elastic collision, the KE of the system goes down. The Universe does not steal that KE. That KE is converted into thermal, chemical or potential energy as the bullet passes through the body creating a wound channel. Simple High School level Physics :neener:.

So when Sean Smith contends that bullets with higher KE have a greater wounding potential, he is correct.

[MrAcheson]

Ryan,

Your Wound Volume*Velocity vs. Kinetic Energy chart is actually a Wound Volume vs. Momentum Chart. You just have to divide the velocities out and multiply kinetic energy by two. It does have a better correlation (Rsquared=.6 instead of .3 with kinetic energy).

I find this interesting because I have always been a momentum guy when it comes to handgun rounds. It better approximates effectiveness against soft targets like people. Now harder targets like body armor really does require energy values.

[Nightcrawler]

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.

That's the first where I've heard anyone say 7.62x51mm is a "notoriously poor stopper". The worst I'd heard anyone say about was that it provided no significant advantage over .223 inside of 100 meters, which I'm not entirely convinced of, but have not the means to test.

In any case, note that in the incident described in Blackhawk Down, I believe the M60 in question was equipped with 7.62x51mm SLAP rounds. Sabot Light Armor Piercing. Basically, it's a .308 sabot-ed down to a .22 caliber, super-high-velocity, armor piercing bullet.

The evidence I've gathered seems to suggest that a very light weight projectile, even moving at high velocities, will perform poorly, despite having high kinetic energy. Whereas a heavier projectile, moving at slightly slower velocities, will do better.

(230 grain @ 900 fps vs 115 grain @ 1250fps, 147 grain @ 2700fps vs. 62 grain @ 3100 fps).

Hard to say for sure, though. The .308 vs. .223 is actually a poor example, though, as a .308 ball round produces rougly twice the kinetic energy of a .223 round. But, as has been said, KE doesn't translate directly into wounding effect. You can walk up to somebody and shove them with both hands, creating more kinetic energy than any handgun bullet, but you won't kill them.

[MrAcheson]

http://www.thehighroad.org/attachment.php?attachmentid=23283&stc=1

I think this momentum plot really tells the story better. You can clearly see the way the individual calibers band with momentum. There just seems to be a lot of scatter in wounding potential within the data that is effecting the spread.

The curve fit is wound volume = 5.532 * momentum incidentally.

[buzz_knox]

That's the first where I've heard anyone say 7.62x51mm is a "notoriously poor stopper". The worst I'd heard anyone say about was that it provided no significant advantage over .223 inside of 100 meters, which I'm not entirely convinced of, but have not the means to test.

Pat Rogers recounts an incident in which he had to shoot an NVA mutliple times with an M-14 at point blank range to put him down. He shot the guy, went to take out his comrades, had to shoot the first guy again after he'd gotten up, shot a couple more comrades, and then finish the first guy off with a couple more rounds.

Also, on www.tacticalforums.com, there is information that standard M80 7.62 mm ball is not as effective as the caliber and power would lead one to believe.

[Graystar]

I don't know that 'energy transfer' is a significant factor with handgun bullets. You want tissue damage and severed blood vessels.I think they’re the same. Like the race car that completely destroys itself to save the life of the driver, energy is transferred by destroying tissue.

Federal EFMJ in .40...is there really anything more to discuss?? ;)

[buzz_knox]

Federal EFMJ in .40...is there really anything more to discuss??

Only that the EFMJ isn't working as advertised, in that it's not as effective as Federal and others led us to believe it would be.

[Graystar]

Only that the EFMJ isn't working as advertised, in that it's not as effective as Federal and others led us to believe it would be.Really? In what way are they not effective? Is there someplace online I can read up on it?

When I heard they expanded reliably I just loaded them into my Glock and haven't thought much of them since, so I'm a tad behind in the latest news.

[buzz_knox]

Check on www.tacticalforums.com. There have been some discussions about lack of expansion with the .40 EFMJ Detroit is issuing.

[RyanM]

[/QUOTE]Energy is always conserved. Energy is neither created nor destroyed. It only changes forms (assuming classic Newtonian physics). In your example, the Universe did not “steal” the “missing energy”. The “missing energy” was used to create a non-elastic collision.

That's pretty much exactly what I said. "the rest of the energy is converted into heat, vibration, noise, etc." I also said "in simplest possible terms," remember. Every time I try to explain how energy works in collisions to people face-to-face, I get extremely blank looks, and sometimes some drool. But "the universe stole it" and "only the energy that tags along with the momentum" are phrases that people can understand.


Your Wound Volume*Velocity vs. Kinetic Energy chart is actually a Wound Volume vs. Momentum Chart. You just have to divide the velocities out and multiply kinetic energy by two. It does have a better correlation (Rsquared=.6 instead of .3 with kinetic energy).

I find this interesting because I have always been a momentum guy when it comes to handgun rounds. It better approximates effectiveness against soft targets like people. Now harder targets like body armor really does require energy values.

Oh yeah, not sure how I missed that, cool.

And actually, it's pressure that matters more when piercing soft body armor. Tensile strength and all that, remember? Though I believe pressure can be roughly calculated by V^2 times some other stuff (I think mass actually cancels out at some point), so it correlates with energy a bit.

I also remember reading a study on the size of the bruise a non-penetrating bullet will make through soft body armor, and momentum correlated the best.


In any case, note that in the incident described in Blackhawk Down, I believe the M60 in question was equipped with 7.62x51mm SLAP rounds. Sabot Light Armor Piercing. Basically, it's a .308 sabot-ed down to a .22 caliber, super-high-velocity, armor piercing bullet.

I keep hearing that claim, with zero sources ever given. Everything I've ever read about SLAP rounds suggests that they were only ever issued for M2s, and the 7.62mm SLAP rounds never left the laboratory. http://www.fas.org/man/dod-101/sys/land/slap.htm

Background: During the 1980s, the Marine Corps invested in both .50 caliber and 7.62 x 51 SLAP concepts. The .50 caliber effort was very successful and extends the light armor capability of the M2 Heavy Machine Gun significantly. The 7.62mm effort was not successful in the M60 and caused catastrophic barrel failures due to in-bore break-up of the sabot and the penetrator puncturing the side of the barrel. Also, its increase in penetration was not on the same order of magnitude as the .50 caliber SLAP's.

There is the M993 AP round, which uses a sub-caliber tungsten penetrator, but the penetrator is encased in the jacket, no sabot to speak of. http://www.fas.org/man/dod-101/sys/land/762ap.jpg

[Graystar]

There have been some discussions about lack of expansion with the .40 EFMJ Detroit is issuing. Thanks for the link. I'll have to research it some more, but I’m not ready to condemn the round yet because of a failure to penetrate a metal plate in someone head, especially when we don’t know the deflection angle. And one out of 11 didn’t penetrate winter clothing? Well I’ve got 20 in my G17 so that ratio works for me!

I did hear that there were some early lots that had quality problems, but I heard Federal had straightened those problems out. In any case I think that ultimately they will be better performers than hollowpoints. But that’s just my own opinion, valued at what you paid for it! ;)

[MrAcheson]

And actually, it's pressure that matters more when piercing soft body armor. Tensile strength and all that, remember? Though I believe pressure can be [iroughly calculated by V^2 times some other stuff (I think mass actually cancels out at some point), so it correlates with energy a bit.
In hard targets you have to worry about fracture mechanics (crack propogation and the like) that aren't as important with squishy elastic stuff like human tissue. Those mechanisms are better modeled with energy.

[coylh]

These gelatins tests are giving me a headache. I don't think this Hole Volume theory explains the real world results well. Look at this data.

Bullet type Weight Velocity Penetration Final diameter Energy Hole volume Source of data
12 guage 437 1513 14 0.78 2220.88566 6.689707397 http://home.snafu.de/l.moeller/Zielwirkung/Frog.html
.30-30 Silvert 170 2020 17.5 0.66 1539.992363 5.9870902 http://home.snafu.de/l.moeller/Zielwirkung/Frog.html
.357 JSP 125 1390 14 0.7 536.1749505 5.387831401 http://home.snafu.de/l.moeller/Zielwirkung/Frog.html
9mm gold dot 124 1192 12.2 0.79 391.1479899 5.980037324 http://www.firearmstactical.com/test_data/9mm/geo9-124+p-g26.htm
.40 Hydrashok 165 943 18.25 0.63 325.7423585 5.688972692 http://www.firearmstactical.com/ammo_data/40s&w.htm
.30-06 SP 150 2923 16.38 0.56 2845.219632 4.034408153 http://home.snafu.de/l.moeller/Zielwirkung/Frog.html
.44 mag Fed 240 1180 20.4 0.55 741.89452 4.846692066 Street Stoppers

The chart shows each load paired with Ryan's Hole Volume index. The labels correspond to the data points going left to right. This index looks really flawed for it to score such different loads so similarly.

BTW, if anyone knows where you can find more gelatin tests with this kind of data, could you let me know; I can't find any more searching the web. Speaking of gelatin, has anyone else noticed that the penetration of the calibration BB is not even close to consistent in a lot of people's tests?

[Zak Smith]

I compiled a list of FBI protocol gel results here
http://apollo.demigod.org/~zak/firearms/fbi-pistol.php

[coylh]

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

[Zak Smith]

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.

[lbmii]

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.

[coylh]

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.

[RyanM]

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.

[griz]

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.

[RyanM]

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.

[lbmii]

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.

http://www.thehighroad.org/attachment.php?attachmentid=23314&stc=1

[lbmii]

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.

http://www.thehighroad.org/attachment.php?attachmentid=23315&stc=1

[lbmii]

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.

http://www.thehighroad.org/attachment.php?attachmentid=23317&stc=1

[lbmii]

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.

http://www.thehighroad.org/attachment.php?attachmentid=23318&stc=1

[lbmii]

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.

http://www.thehighroad.org/attachment.php?attachmentid=23319&stc=1



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.

[coylh]

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

[coylh]

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

[Zak Smith]

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.
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.

[Cosmoline]

Pat Rogers recounts an incident in which he had to shoot an NVA mutliple times with an M-14 at point blank range to put him down. He shot the guy, went to take out his comrades, had to shoot the first guy again after he'd gotten up, shot a couple more comrades, and then finish the first guy off with a couple more rounds.

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.

[coylh]

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

[RyanM]

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.

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.

[Zak Smith]

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.

[Cosmoline]

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.

[coylh]

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

[coylh]

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

[Clean97GTI]

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.

[coylh]

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

But we're stuck with lead pellets.

[RyanM]

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.

Number one is what actually happens. Number two almost never happens. Ideally, bullets would have little rocket engines on the back so they wouldn't lose any velocity while penetrating, and actually could continue to expand.

[MrAcheson]

Ideally, the bullet would strike the target, expand to encompass its entire cross sectional area, penetrate through the target, stop 0.001" behind it, and fall to the ground harmless.

What you should get out of this is that energy is not a good handgun performance metric. Momentum is better. You can't just keep increasing velocity on a little bullet and expect it to do substantially more damage. You need to make the bullets bigger too.

That and expansion is important. If one HP reliably expands larger than another, go with the bigger one.

[coylh]

How are you calculating momentum for these charts?

[MrAcheson]

Momentum is projectile weight*velocity. Which weights/velocities you use don't matter much. It just introduces a scaling factor to account for unit changes into the final equation.

[lbmii]

Correct me if I am wrong because I am going by memory.

Momentum = mass in grains, times velocity in FPS, divided by 225120

Energy = mass in grains, times velocity in FPS, times velocity in FPS, divided by 450400

[lbmii]

You might be a gunnut if:

You can recite a bullet momentum formula from memory but you have no clue what your bank account number is.

[RyanM]

It's a lot easier to remember (albeit slower to type into a calculator) if you know the individual components of the numbers and what they actually are:

( mass (gr) / 7000 / 32.174 / 2 ) * vel^2 for energy, which shortens to mv^2/450436.

( mass (gr) /7000 / 32.174) * vel for momentum, or mv/225218.

/7000 to get grains to pounds, /32.174 to convert pounds to slugs.

[MrAcheson]

Or you could just use the IPSC "power factor" and go with grains*fps/1000. This is a momentum measure too.

[lbmii]

RyanM

It's been 18 years since Physics class. What is the proper way to label Momentum and Energy?

[RyanM]

It's been 18 years since Physics class. What is the proper way to label Momentum and Energy?

In the English system, Energy is in Foot-Pounds, and I believe Momentum is in Pounds*Feet/Second.

It's a little confusing because in both instances, "Pound" refers to pounds-force, not pounds-mass. 1 pound-force will accelerate 1 pound-mass by ~32.174 fpsps (acceleration due to gravity is 32.174 fpsps [ft/s^2, ft/s/s, ft*s^-2, or feet per second per second]), and 1 pound-mass exerts 1 pound-force on the ground at sea level.

You might also hear of the units foot-poundals and poundals*feet/second; those use the poundal, which is a unit of force which accelerates 1 pound-mass by 1 fpsps. The slug is the "official" unit of mass, and is equal to 32.174 pounds-mass; so 1 pound of force accelerates 1 slug of mass by 1 fpsps.


same momentum as a good 223 SP, and 4x the frontal area.

I've said it about 20 times now. The analysis is pistol rounds only because rifle bullets make efficient use of fragmentation and temporary cavitation, while handgun rounds lack the force, not energy, to do so. Thus comparing handguns to rifles is like comparing apples and crab-apples.

[Brasso]

I'm a mathmatical failure, but since velocity is a major player in expansion, and since a bullet with more momentum will retain it's velocity longer wouldn't it make sense that a bullet with more momentum be more reliable at expanding?

[RyanM]

I'm a mathmatical failure, but since velocity is a major player in expansion, and since a bullet with more momentum will retain it's velocity longer wouldn't it make sense that a bullet with more momentum be more reliable at expanding?

Energy and momentum both have velocity in them. It's just that increasing velocity has different effects.

Doubling velocity while keeping weight the same will double momenum, but quadruple energy.

[Brasso]

I understand that, but a heavier bullet (I should have said heavier instead of more momentum) has more momentum due to weight so will not slow down as fast as a lighter bullet moving faster, assuming same starting momentum. So for a given caliber the heavier bullet will retain its velocity longer and should be more reliable at expanding.

[Yooper]

Penetration is the desired effect of a bullet after leaving the barrel of a firearm. Sectional density, velocity, and bullet construction determine penetration, it is independent of caliber.

The primary consideration of bullet behavior is penetration, either more or less. Even varmint bullets penetrate somewhat or they would not expand. Penetration is necessary for expansion.

Expanding bullets of various types are designed to expand at a range of velocities which depends upon their construction. Hollow points expand rapidly, round nose soft points and spire points less rapidly. Some bullets are designed to limit expansion with a cross-member of jacket material.

Non-expanding bullets are designed to hold together and to retain their shape as much as possible. These bullets penetrate the deepest, often exiting the target.

Penetration for either expanding or non-expanding is a function of sectional density, velocity, and the medium it is fired into. Air is also a medium and we can draw a few conclusions from bullet behavior in it. Hunting bullets are manufactured to optimum performance specs in game animals.

In the case of expanding bullets, depending on the optimum velocity range of its design, slower than optimum velocity will promote penetration and retard expansion, faster than optimum velocity will promote expansion at the expense of penetration, sometimes to the point of fragmentation. An expanding bullet is decreasing its sectional density as it expands.

In the case of non-expanding bullets, and assuming absolutely no bullet distortion, each sectional density has an optimum penetration beyond which increased velocity will produce greater penetration, but not at a proportional rate. It is a point of diminishing return, and the greater the sectional density, the greater the velocity before this point is reached. In the case of 44 mag, 250 gr hardcast, velocities above 1100 fps start producing a diminishing return, for 300 gr hardcast the optimum velocity is about 1300 fps. We soon reach the limiting factors of pressure and recoil with the heavier bullets.

[BluesBear]

One thing that no one has mentioned is that expanding handgun bullets, with the exception of Federal EFMJ, enter, expand to their largest possible diameter and then, as the petals fold back get smaller.
This is also why we see a large cavity, early on, tapering down to final bullet diameter in Jell-O testing.

I think that the larger final diameter the bullet can maintain the better the overall performance will be.

[RyanM]

Wow, old thread. Anyways, though, in most cases the petals are in continuous motion for the first 2-3" of penetration. Or less. Federal used to have some advertisements with high-speed photography of a Hydra-Shok being fired through a 1" sliver of gelatin, and exiting completely expanded.

So by the time the bullet has gone 3" (at most), the petals are already folded back. It's really the velocity, and the efficiency of crushing gelatin (or tissue) which causes the hole to taper.

Pretty much all the data on this thread is outdated, though. Using my new equations which take the temporary cavity and associated tearing into effect, here's a graph comparing energy to wound volume.

http://www.thehighroad.org/attachment.php?attachmentid=42110&stc=1&d=1152732543

So, energy is the ability to do work. But whether or not the bullet makes the maximum sized wound depends on bullet design, and whether the bullet is driven to its intended velocity. As stated before.

On the other hand, here's a chart comparing the peak pressure wave (calculated per Michael Courtney and team's research) to wound volume.

http://www.thehighroad.org/attachment.php?attachmentid=42111&stc=1&d=1152732543

Pretty good correlation I'd say.

[Michael Courtney]

On the other hand, here's a chart comparing the peak pressure wave (calculated per Michael Courtney and team's research) to wound volume.



Pretty good correlation I'd say.

Nice correlation, but there is room for improvement. The pressure wave does indeed cause wounding beyond the expanded bullet diameter early in the wound channel. This contributes to what Peters calls "prompt damage." See

Peters "A Mathematical-Physical Model of Wound Ballistics". J. Trauma
(China) 6 (Suppl): 303, 1990.


However, at some point in the penetration as the bullet transfers energy more slowly, the pressure wave decreases below the damage threshold of the tissue, and the direct crush mechanism dominates. I believe that an even more accurate correlation is possible by modeling the wound volume as a combination of these two effects. The non-trivial part is understanding the transition from the depths dominated by pressure wave contributions to wound volume to the depths dominated by the direct crush mechanism.

Michael Courtney

[Old Pete]

Please do not describe my work in wound ballistics until you understand it well enough to describe it correctly.

Carroll Peters (Old Pete)

[thales]

*


Old Pete,

For those of us who have no easy access to your article, would you care to summarie it and Michael Courtney's error in describing it? Perhaps you could post the relevant text.

Thanks


*

[jeepmor]

Please do not describe my work in wound ballistics until you understand it well enough to describe it correctly.

Carroll Peters (Old Pete)


I think Mr Courtney, IIRC, is currently studying this very subject matter at MIT. I think he's well qualified to do so, maybe one of the most qualified. If I'm wrong about him studying at MIT, my apologies. But that school turns out the best muscle brains in the world and I've read some of his threads. He knows his subject matter on ballistics better than nearly any other poster I've read on THR. He is certainly more scientific than any gun rag analysis of anything I've read.

BTW folks - charts without axis labels drops your grade by one point, B's for everyone.

jeepmor

[Michael Courtney]

I think Mr Courtney, IIRC, is currently studying this very subject matter at MIT. I think he's well qualified to do so, maybe one of the most qualified. If I'm wrong about him studying at MIT, my apologies. But that school turns out the best muscle brains in the world and I've read some of his threads. He knows his subject matter on ballistics better than nearly any other poster I've read on THR. He is certainly more scientific than any gun rag analysis of anything I've read.

BTW folks - charts without axis labels drops your grade by one point, B's for everyone.

jeepmor

My PhD is in Physics from MIT. I am currently a Physics Professor and Director of the Forensic Science Program at Western Carolina University. My research is conducted as a part of the Ballistics Testing Group. I hope to have a web site functional through the university by the end of the fall semester.

However, qualifications alone do not guarantee perfect understanding of the literature. I may well have misunderstood or misrepresented the work I cited. It is not uncommon for a scientist to misunderstand the work of another. I've made a private request of the author for clarification.

Looking back at my citation, I realize that there is ambiguity regarding what part of the assertions are contained explicitly in the reference, and what part of the assertions are ideas from our research group. Let me clarify.

Nice correlation, but there is room for improvement. The pressure wave does indeed cause wounding beyond the expanded bullet diameter early in the wound channel. This contributes to what Peters calls "prompt damage." See

Peters "A Mathematical-Physical Model of Wound Ballistics". J. Trauma
(China) 6 (Suppl): 303, 1990.

However, at some point in the penetration as the bullet transfers energy more slowly, the pressure wave decreases below the damage threshold of the tissue, and the direct crush mechanism dominates. I believe that an even more accurate correlation is possible by modeling the wound volume as a combination of these two effects. The non-trivial part is understanding the transition from the depths dominated by pressure wave contributions to wound volume to the depths dominated by the direct crush mechanism.


The main reason for the citation is the definition of prompt damage as "Compression, shearing, and stretching of tissue in the immediate vicinity of the projectile." "This damage occurs . . . typically on the order of 10 microseconds" which is much faster than formation of the full temporary cavity.

My assertion that "The pressure wave does indeed cause wounding beyond the expanded bullet diameter early in the wound channel." is the result of our work and is not asserted directly in the referenced article. However, I believe it can be reasonably inferred from Equation 7 on page 311.

This equation says that the cross sectional area of the prompt damage is proportional to the retarding force (dE/dx) and inversely proportional to the rupture modulus. Since there is nothing in the equation limiting the cross sectional area of the prompt damage to the cross sectional area of the bullet, it is easy to see that there must be some combination of retarding force, drag coefficient, and velocity for which the cross sectional area of the prompt damage exceeds the cross sectional area of the bullet.

This action at a distance (damage without direct crush) is conveyed by the outward propagating pressure disturbance which we call the pressure wave, which is also proportional to the retarding force, (dE/dx), as described in my earlier post, _The Physics of the Ballistic Pressure Wave_.

Lets throw some sample numbers to give a concrete example. The damage threshold for tissue can be expressed in PSI, and one number in the literature is around 600 PSI. However, we know that this can vary depending on the strain rate, so let's be conservative and double our damage threshold to 1200 PSI. To make the numbers easy consider a projectile which has a maximum rate of energy loss of 100 ft-lbs in 1 inch of penetration. This results in an instantaneous retarding force of 1200 pounds. Consequently, the expected cross sectional area of prompt damage at this point is 1 square inch. If the hole has a circular cross section, then the diameter of the local prompt damage is 1.13", which is considerably larger than the tissue that could be directly crushed by most bullets.


The assertions of the last paragraph which begins,

However, at some point in the penetration as the bullet transfers energy more slowly, the pressure wave decreases below the damage threshold of the tissue, and the direct crush mechanism dominates.

are my own and I do not believe are explicitly stated in the reference.

There is also some important discussion on page 314 of the reference demonstrating the basis for concluding that the wounding under consideration is "prompt damage" rather than the result of temporary cavitation.

Michael Courtney

[MrAcheson]

To make the numbers easy consider a projectile which has a maximum rate of energy loss of 100 ft-lbs in 1 inch of penetration. This results in an instantaneous retarding force of 1200 pounds.

Correct me if I'm wrong, but shouldn't this be an average retarding force not an instantaneous one? I suppose the timescale is short, but not short in relation to the timescale of the problem in question. But that is a nit.

I'm curious, how much of this example is a simplification? You seem to be assuming a form of conservation of mechanical energy and I don't think I can agree with that. I would rather handle this problem as one of conservation of momentum which probably works as well and has the advantage that momentum must be conserved. If any significant portion of the bullets energy is converted to heat or another form of energy through visco-elastic effects, then you're going to start overpredicting damage pretty quickly, no?

Way back when I did bullet impact work, we tried to keep everything in terms of momentum because we found that using energy involved a lot more assumptions.

[Michael Courtney]

Correct me if I'm wrong, but shouldn't this be an average retarding force not an instantaneous one? I suppose the timescale is short, but not short in relation to the timescale of the problem in question. But that is a nit.

Computing the average force over each inch of penetration is a pretty good estimate of the actual instantaneous force (10% or so error). It is certainly a much better estimate of instantaneous force than the average force over the whole penetration depth.

I'm curious, how much of this example is a simplification? You seem to be assuming a form of conservation of mechanical energy and I don't think I can agree with that.

Mechanical energy only needs to be approximately conserved for a few microseconds for Equation 7 in the reference to hold, because the timescale of prompt damage is less than 10 microseconds. The agreement that the model including Equation 7 finds with a number of empirical data sets, as well as the rest of the paper suggests that very little mechanical energy is lost in the short timescale in question. The typical times (several milliseconds) of temporary cavitation suggest that to the degree that mechanical energy is not conserved (conversion to heat), it is lost over a much larger time period (milliseconds). It's no huge stretch to infer that in the timescale of less than 10 microseconds, less than 2% of mechanical energy will be lost to heat.

I would rather handle this problem as one of conservation of momentum which probably works as well and has the advantage that momentum must be conserved. If any significant portion of the bullets energy is converted to heat or another form of energy through visco-elastic effects, then you're going to start overpredicting damage pretty quickly, no?

One runs the risk of overpredicting effects that occur on the same timescale as elastic effects (milliseconds), but only if one assumes energy conservation for these. The referenced paper accurately models temporary cavitation because it does not depend on mechanical energy conservation for this part.

The central idea to the retarding force approach is that the retarding force is equal to the local rate of the bullet's energy loss. dE/dx. This does not depend on conservation of mechanical energy, but only on the work energy theorem. The retarding force need not be conservative.

As the retarding force approach is broadened to predict temporary cavitation (as Peters does) or pressure wave effects (what I am doing), mechanical energy conservation is not required, but merely consistency in time/distance scales of mechanical energy loss in the systems under study.

Way back when I did bullet impact work, we tried to keep everything in terms of momentum because we found that using energy involved a lot more assumptions.

Only if you use mechanical energy conservation over a time/length scale over which it does not apply. A lot of very solid physics can be done using energy without mechanical energy conservation.

Michael Courtney

[MrAcheson]

Interesting and it sounds like you have things well in hand. Thanks for the reply.

[trapperjohn]

where is the evidence that your assumption that wound volume correlates to wounding ability? personaly, i would not consider that a valid assumption.
what made you choose that over surface area or depth of penetration?

[P95Carry]

your assumption that wound volume correlates to wounding ability
John - chipping in briefly as the amateur ;)

I can conceive of very deep penetration along with minimal wound channel volume increase - not necessarily causing major damage. Perhaps a smaller cal at modest velocity - a ''clean'' narrow channel perhaps - the oft survivable wounds.

If OTOH there is large wound volume due to temporary cavitation - elastic limits being at least in part exceeded, then it does seem that ''damage'' is increased, thru mainly tear/rupture mechanisms. Displace structures enough thru a volumetric cavity increase event and internal surface area must by default increase too - disregarding surface area from an external POV.

Just musing - that's all :)