A question to Doc - the importance of expansion to incapacitation

[BBMW]

Doc,

Assume the numbers below come out of a properly done IWBA standard 4 layer denim test in properly calibrated ballistic gelatin. I'm intentionally not dealing with barrier penetration issues (auto glass, steel, wallboard, etc.)

Take two 9mm rounds. Both penetrate past 12". For the first hypothetical, they penetrate equally One expands to .5", the other expands to .6" I look at the math of this, calculate the frontal areas of the two bullets, and see that the larger bullet has a 44% larger frontal area. (Note, I'm taking frontal area as a simple circle to calculate area based on diameter.) I take this as giving it 44% advantage in destroyed tissue, and figure this most have some significant increased effect on incapacitating capability. Is this thinking correct, or am I missing something? If it's the latter, what am I missing.

In the second hypothetical, everything is the same as the first one except penetration. The bullet that expands to .6" will penetrate to 13" While the bullet that expands to .5" penetrates to 16". If I now take the frontal area and multiply by penetration, I get crush cavity volume. The bigger bullet still has an advantage here by about 17%. But the other factor in penetration is that the deeper penetrating round might hit something the shallower penetrating round wouldn't. But given the fact that both meet the minimum standard, which, if either, would have a better chance of a quick incapacitation?

Let me know what you think. Thanks.

[DocGKR]

Ah....as in most things in life, simple models don't fully reflect the complex variables existing in real life and the question is not answerable with any degree of specificity.

For example, which projectile has a sharper leading edge and what are the shapes like?

37014

All of the above have the same average expansion, but the third one from the left probably offers the most efficient cutting.

In general, if two handgun projectiles have EXACTLY the same parameters in every other metric, then the one which directly crushes more tissue will tend to be more effective.....most of the time.

[BBMW]

Thanks Doc.

Yes, I realize my analysis might be a bit simplistic. For bullets that expand in a snowflake (for lack of a better term) pattern, vs circular, I take the diameter as the average width of the expanded petals, on the assumption that tissue in the Vs between them will be compromised by the cutting action you describe.

[45dotACP]

Are we making the assumption that all other variables are truly equal or would you consider other variables more important?

I'd think a difference of .1 inches would lead me to consider which of the two rounds were more accurate or softer shooting in the firearm I chose but that's just me.

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[BBMW]

Does it some more consequential if it's stated as a 40+% increase in frontal area? I think that's the question, how much difference does this aspect make, so that it could be evaluated against the other characteristics of the round, including the ones that you point out. This also applies to evaluating different calibers.

It might not be a big deal. I'm not in a position to know. The good doctor is.


Are we making the assumption that all other variables are truly equal or would you consider other variables more important?

I'd think a difference of .1 inches would lead me to consider which of the two rounds were more accurate or softer shooting in the firearm I chose but that's just me.

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[Duelist]

.1” difference in expansion, by itself, does not strike me as particularly significant. 2 bullets from the same box might have that much variance. Striking a bone vs not striking a bone might cause some variance.

What I think about more: Does that bullet penetrate to a depth I want for that application? Does it reliably expand? Does it function 100% in the firearm(s) I intend to use it in? Does it hit within an acceptable dispersion from POA from that firearm? If all of those are met, I will not find any purpose in worrying about .1” difference in expansion.

[the Schwartz]

For bullets that expand in a snowflake (for lack of a better term) pattern...

May I recommend the term 'stellate' for describing the expansion of bullets like the HSTs and the Barnes XPBs?

[BBMW]

I've never heard that term used before, but, looking it up, it does fit. I wonder how many would actually know what it means.


May I recommend the term 'stellate' for describing the expansion of bullets like the HSTs and the Barnes XPBs?

[Polecat]

I would think most damage is done during expansion prior to thepetals folding
All the back giving a “leading” edge. So are the terminal dimensions of expansion actually
Incorrectly measuring a more “true” expansion.

Example, if you fold the expanded petals back to their most open position and then take the measurement, that woul
Give a larger expanded dimension?

[DocGKR]

Most properly designed handgun projectiles offer full expansion within the first 1-3" of travel in tissue. This has been previously repeatedly proven by shooting thin 3" blocks of properly fabricated tissue simulant and recovering the projectiles.....

[the Schwartz]

I've never heard that term used before, but, looking it up, it does fit. I wonder how many would actually know what it means.

I imagine that many might know the term. It is a term used frequently in the medical profession to describe the shape of wounds, lacerations, types of spinal nerve structure like stellate ganglion, etc.

[BBMW]

Doc, a related issue, which you allude to, is pointed out by the picture you posted. Taking the last to bullets in the picture (the all copper and the one immediately to its right), I would consider the expanded diameter to be the average of the with of the expanded petals. I would not in include the width of the valleys between the petals in the calculation. I would think, as one of those bullets passed thought tissue, the tissue that fit into those valleys would be highly compromised and likely shredded, contributing the wounding/incapacitation effect of the bullet. This would mean that for purposes of determining crush cavity volume, the bullets to the far left would not be equivalent to bullets to the right. Does this make sense to you?


Ah....as in most things in life, simple models don't fully reflect the complex variables existing in real life and the question is not answerable with any degree of specificity.

For example, which projectile has a sharper leading edge and what are the shapes like?

37014

All of the above have the same average expansion, but the third one from the left probably offers the most efficient cutting.

In general, if two handgun projectiles have EXACTLY the same parameters in every other metric, then the one which directly crushes more tissue will tend to be more effective.....most of the time.

[DocGKR]

The standardized method for reporting the recovered diameter of a projectile is to average the widest and narrowest diameters.

[Schmetallurgy]

I would think one advantage to a sharp and stellate frontal shape is that for a given average frontal area and its resulting penetration depth, the larger max radius in comparison to a contiguous mushroom profile would increase the likelihood of severing a critical and perhaps relatively elastic structure the narrower, smoother mushroom profile might miss or push aside.

I would also think an advantage to a large frontal surface beyond simple crush volume is the less resistive void, after elastic rebound, to blood flow rate from the surrounding tissue.

[John Hearne]

Doc,

Any thoughts on Poiseuille's Law and this topic. I've been told "the volume flowrate is given by the pressure difference divided by the viscous resistance. This resistance depends linearly upon the viscosity and the length, but the fourth power dependence upon the radius is dramatically different." Again, I was told a leak caused by an unexpanded 45 would drain ~2.6 times faster than an unexpanded 9mm. Supposedly the increased viscosity of blood exacerbates this.

Any thoughts?

[the Schwartz]

Doc,

Any thoughts on Poiseuille's Law and this topic. I've been told "the volume flowrate is given by the pressure difference divided by the viscous resistance. This resistance depends linearly upon the viscosity and the length, but the fourth power dependence upon the radius is dramatically different." Again, I was told a leak caused by an unexpanded 45 would drain ~2.6 times faster than an unexpanded 9mm. Supposedly the increased viscosity of blood exacerbates this.

Any thoughts?

I am not Doc, but a little 'back-of-the-napkin' math answers the question....

Since the dynamic viscosity of whole blood varies between 2.75 and 3.75 cP (at 98.6°F) calculating the volume flux for an unexpanded .45 FMJRN and a 9mm FMJRN is fairly straightforward. The effect of dynamic viscosity 'cancels itself out' as we are comparing the same fluid in both cases (that is, .45 vs. 9mm FMJRNs) and can assume that viscosity may be treated as a constant. Selecting the 'high end' (of 3.75 cP) of the typical viscosity range as a ''worst case scenario''....

The equation is Q = (ΔP п r4) ÷ (8 η l)

For the .45 ACP FMJRN, Q = (ΔP п r4) ÷ (8 η l) we assume a 'normal' blood pressure differential (ΔP) of 40 mmHg (or about 5,332.895 Pa), which is the difference of the 'normal' 120/80 blood pressure reading that we are accustomed to seeing. This value is ΔP in the equation. We'll assume that the FMJRN wound channel length is 12'' (or 30.48 cm), that it exits the abdomen and that only the exit wound bleeds.

So...if ΔP is 5,332.895 Pa

.45ACP FMJRN (diameter is taken as 0.4515'' or 1.14681 cm)

(5,332.895 x п x 0.5734054) ÷ (8 x 3.75 x 30.48) = Q = 1.980718 cm3 per heart beat

9mm FMJRN (diameter is taken as 0.355'' or 0.9017 cm)

(5,332.895 x п x 0.450854) ÷ (8 x 3.75 x 30.48) = Q = 0.757016 cm3 per heart beat

Since 1 cm3 equals 1 ml volume, we can estimate the rate of blood loss in some one who has been shot once with each round.

We'll assume that the person's heart rate jumps to an ''elevated'' rate of 140 bpm, that their blood pressure increases to 165/110, that constant uninterrupted blood flow exists, that no clotting occurs and that no pressure is applied to the wound. If a large male has a total blood volume of 5.5L, we can estimate when unconsciousness occurs (50% loss of that 5.5L volume or 2.75 L). In this case―the same penetrating 12'' wound through the abdomen as above―the pressure differential (ΔP) is 7,332.73 Pa.

For the .45ACP FMJRN (diameter is taken as 0.4515'' or 1.14681 cm)

(7,332.73 x п x 0.5734054) ÷ (8 x 3.75 x 30.48) = Q = 2.723487 cm3 per heart beat @ 140 bpm = a loss of 0.381288 Liters/minute which means that 50% loss of blood volume leading to unconsciousness would occur 7 minutes 13 seconds after the infliction of the wound.

For the 9mm FMJRN (diameter is taken as 0.355'' or 0.9017 cm)

(7,332.73 x п x 0.450854) ÷ (8 x 3.75 x 30.48) = Q = 1.040897 cm3 per heart beat @ 140 bpm = a loss of 0.145726 Liters/minute which means that 50% loss of blood volume leading to unconsciousness would occur 18 minutes 52 seconds after the infliction of the wound.

Of course, there are other factors that are not addressed here and cannot be predicted. Soft tissues and visceral fat also tends to 'seal up' or 'close over' such wounds and restricts (plugging/obstructing) blood flow in many cases. Most people also tend not to let the wound bleed and will apply pressure to the entry and exit wound (if there is one). Clotting can also occur with or without medical intervention.

[DocGKR]

Never seen any mathematical equation or computer model which accurately accounts for all the variations in physiology which can and do occur with projectile tissue interactions. As noted, tissue retraction, clotting, blood pressure, are just a few of the variables that dramatically alter the wounding effects.

[the Schwartz]

Never seen any mathematical equation or computer model which accurately accounts for all the variations in physiology which can and do occur with projectile tissue interactions. As noted, tissue retraction, clotting, blood pressure, are just a few of the variables that dramatically alter the wounding effects.

Yes, beyond doing a 'back-of-the-napkin' exercise creating such a model is certainly not anything that I would ever want to attempt. The vast assumptions required would render it cumbersome and inaccurate at best.

[TiroFijo]

Where do you find a blood vessel large enough to sustain a 9 mm or 45 hole cleanly, not tearing apart? How likely is the probability of that happening? How much of the frontal area of the torso has such vessels?

[the Schwartz]

Where do you find a blood vessel large enough to sustain a 9 mm or 45 hole cleanly, not tearing apart? How likely is the probability of that happening? How much of the frontal area of the torso has such vessels?

There are vessels large enough to supply such flow in the abdomen; the abdominal aorta and vena cava come to mind. The rest of those questions are dependent upon the complex structure of the human body and the associated probabilities of striking such vessels. As I stated above, such a task is way too vast to pursue beyond the 'back of the napkin' calculations and the assumptions that I made.

[TiroFijo]

I know... my comments were made tongue-in-cheek to show how "low percentage" such targets are in reality, and combined with the variables cited by Doc make trying to estimate X vs Y caliber effects in bleeding just an academic (worthless?) exercise.

[the Schwartz]

I know... my comments were made tongue-in-cheek to show how "low percentage" such targets are in reality, and combined with the variables cited by Doc make trying to estimate X vs Y caliber effects in bleeding just an academic (worthless?) exercise.

Worthless? Maybe, but it can provide some insight, too.

Fun (if you like mathematical modeling like I do)? Yep! :cool: