Do handgun JHPs continue to expand in lungs? How quickly?

[GhostCan]

Have a question for those who are well acquaintanced with terminal ballistics.

Thoracic cavity shots probably account for most handgun rounds that can be expected to contribute to quick physiological incapacitation. On the other hand, the majority of bullets that hit (for example) the intestines, probably are not very important for this purpose.

With this being noted, the lungs make up most of the space within the thoracic cavity, and regardless of whether the incapacitating damage is actually produced within them, the projectiles will likely have to travel through lung tissue when/before they hit vital structures. As a whole, the spatial density of lungs is much lower than muscle, 10% ordnance gelatin, or water.

I believe it was said in one of the IWBA issues that hydraulic expansion of JHPs in gelatin/muscle would primarily be expected to occur when the bullet is traveling above a minimum of 600 ft/s, as below this speed, the pressure encountered by the projectile would likely be inadequate to overcome the deformation resistance of lead. Since hydraulic pressure presumably has a direct correlation with density, it seems like the velocities required to continue expansion in a much less dense medium (in this case, the lungs) would be much greater - perhaps greater than the remaining velocities of service caliber handgun rounds by the time they reach these organs.

On the other hand, the lungs are not truly homogeneous, rather they are formed of denser tissue and fluid interspersed with air pockets; so perhaps this "minimum deformation velocity" doesn't actually change drastically, rather the bullet simply mushrooms slower. I am also not intimately familiar with bullet engineering, and maybe there are some modern designs that can utilize shear resistance (where lung and muscle are roughly the same, if I recall correctly) to expand.

I think Dr. Roberts stated at one point that most handgun bullets are already fully expanded after traveling through 2" of ballistic gelatin. Since this seems to be roughly the thickness of the average chest wall, in most cases I expect it would not matter if JHPs could continue to expand afterwards - they are fully expanded by the time they reach the lungs. On the other hand, you might have a thin individual with a very narrow chest wall wearing very heavy clothing, and in this case the bullet has less opportunity to fully expand and likely does so at a slower rate.

Having said that, could a service caliber handgun JHP continue to expand further if the thickness of the preceding chest wall were inadequate to accomplish full expansion? Does it stop expanding at that point, and whatever it already has is what it's stuck with? Or do modern JHP designs expand so quickly that even a <1.5" chest wall covered in dense clothing would be sufficient?

[the Schwartz]

Have a question for those who are well acquaintanced with terminal ballistics.

Thoracic cavity shots probably account for most handgun rounds that can be expected to contribute to quick physiological incapacitation. On the other hand, the majority of bullets that hit (for example) the intestines, probably are not very important for this purpose.

With this being noted, the lungs make up most of the space within the thoracic cavity, and regardless of whether the incapacitating damage is actually produced within them, the projectiles will likely have to travel through lung tissue when/before they hit vital structures. As a whole, the spatial density of lungs is much lower than muscle, 10% ordnance gelatin, or water.

I believe it was said in one of the IWBA issues that hydraulic expansion of JHPs in gelatin/muscle would primarily be expected to occur when the bullet is traveling above a minimum of 600 ft/s, as below this speed, the pressure encountered by the projectile would likely be inadequate to overcome the deformation resistance of lead. Since hydraulic pressure presumably has a direct correlation with density, it seems like the velocities required to continue expansion in a much less dense medium (in this case, the lungs) would be much greater - perhaps greater than the remaining velocities of service caliber handgun rounds by the time they reach these organs.

On the other hand, the lungs are not truly homogeneous, rather they are formed of denser tissue and fluid interspersed with air pockets; so perhaps this "minimum deformation velocity" doesn't actually change drastically, rather the bullet simply mushrooms slower. I am also not intimately familiar with bullet engineering, and maybe there are some modern designs that can utilize shear resistance (where lung and muscle are roughly the same, if I recall correctly) to expand.

I think Dr. Roberts stated at one point that most handgun bullets are already fully expanded after traveling through 2" of ballistic gelatin. Since this seems to be roughly the thickness of the average chest wall, in most cases I expect it would not matter if JHPs could continue to expand afterwards - they are fully expanded by the time they reach the lungs. On the other hand, you might have a thin individual with a very narrow chest wall wearing very heavy clothing, and in this case the bullet has less opportunity to fully expand and likely does so at a slower rate.

Having said that, could a service caliber handgun JHP continue to expand further if the thickness of the preceding chest wall were inadequate to accomplish full expansion? Does it stop expanding at that point, and whatever it already has is what it's stuck with? Or do modern JHP designs expand so quickly that even a <1.5" chest wall covered in dense clothing would be sufficient?

To answer your question, ''Do handgun JHPs continue to expand in lungs?'', in one word: Yes.

In accordance with the Bernoulli pressure equation, as long as the bullet's velocity is sufficient to produce dynamic pressure (P) that exceeds the yield strength of the bullet's alloy composition expansion/deformation will occur. The density of lung tissue (ρ_T) ranges from about 0.40 g/cm³ (inflated) to 1.050 g/cm³ (deflated) so determining the minimum velocity necessary to drive expansion of a given alloy is a straight-forward process.

Manufacturers control the yield strength of bullets through the manipulation of alloy content.

For example, ignoring the hoop tension forces created by the bullet's jacket that resist expansion for the time being, a 9mm 147-grain JHP made of 2% antimonial lead, would have a yield strength of 3,480 psi (24.0 MPa) and require an impact velocity of—

Re-arranging the Bernoulli pressure equation...

For fully inflated lung tissue: √[2P ÷ ρ_T] = √[(2 x 24,000,000 N/m²) ÷ 400 kg/m³] = 346.4 m/s = 1,136.5 fps for expansion to occur

For fully deflated lung tissue: √[2P ÷ ρ_T] = √[(2 x 24,000,000 N/m²) ÷ 1,050 kg/m³] = 213.8 m/s = 701.5 fps for expansion to occur

Using the Q-model to estimate the remaining velocity of a hypothetical 9mm 147-grain JHP with an impact velocity of 1,000 fps that expands to 0.65'' after passing through 2 inches of human tissues before encountering lung tissue, its velocity would decrease to approximately 750 fps making additional expansion in fully inflated lung tissue impossible and somewhat probable in fully deflated lung tissue.

[Dr_Thanatos]

To answer your question, ''Do handgun JHPs continue to expand in lungs?'', in one word: Yes.

From my experience, the answer is also yes. If the bullet didn't expand, the reason has nothing to do with the lungs.


Also, math is hard.

[the Schwartz]

Also, math is hard.

It can be.

[5pins]

So shoot them as they exhale.

[GhostCan]

To answer your question, ''Do handgun JHPs continue to expand in lungs?'', in one word: Yes.

In accordance with the Bernoulli pressure equation, as long as the bullet's velocity is sufficient to produce dynamic pressure (P) that exceeds the yield strength of the bullet's alloy composition expansion/deformation will occur. The density of lung tissue (ρ_T) ranges from about 0.40 g/cm³ (inflated) to 1.050 g/cm³ (deflated) so determining the minimum velocity necessary to drive expansion of a given alloy is a straight-forward process.

Manufacturers control the yield strength of bullets through the manipulation of alloy content.

For example, ignoring the hoop tension forces created by the bullet's jacket that resist expansion for the time being, a 9mm 147-grain JHP made of 2% antimonial lead, would have a yield strength of 3,480 psi (24.0 MPa) and require an impact velocity of—

Re-arranging the Bernoulli pressure equation...

For fully inflated lung tissue: √[2P ÷ ρ_T] = √[(2 x 24,000,000 N/m²) ÷ 400 kg/m³] = 346.4 m/s = 1,136.5 fps for expansion to occur

For fully deflated lung tissue: √[2P ÷ ρ_T] = √[(2 x 24,000,000 N/m²) ÷ 1,050 kg/m³] = 213.8 m/s = 701.5 fps for expansion to occur

Using the Q-model to estimate the remaining velocity of a hypothetical 9mm 147-grain JHP with an impact velocity of 1,000 fps that expands to 0.65'' after passing through 2 inches of human tissues before encountering lung tissue, its velocity would decrease to approximately 750 fps making additional expansion in fully inflated lung tissue impossible and somewhat probable in fully deflated lung tissue.

Thank you for taking the time to help me out.

I assume in most cases that the average density of a living attacker's lungs will be closer to the inflated figure since they will naturally contain some air even when breathing out. However, it seems like the bullet would compress tissue while moving forward - this should, at least theoretically, result in the creation of a mass of flesh in the hollowpoint cavity and/or just in front of the bullet that is denser than the medium itself.

In other words, the bullet may be "deflating" the lung tissue right in front of it. Exactly how much and to what extent is the part that I don't know.

Could this be relevant? I suppose this depends on 1) how quickly any crushed tissue gets shucked off to the side rather than remaining in front of the bullet, 2) how much pressure the bullet exerts on tissue ahead of it that it has no directly contacted yet, 3) whether there is any difference in its ability to compress inflated lung vs deflated lung or muscle.

If there is no difference in #3 then the required expansion velocity in inflated lung should follow normal calcs if the required expansion velocity in deflated lung/muscle is roughly known. However it seems like there could plausibly be some substantial difference since an air-filled mass of elastic tissue seems inherently more compressible than the same elastic tissues that don't contain significant quantities of air; after all, its ability to change volume/collapse easily is part of why lung density can vary so much in the first place.

I guess for many people this is probably an excessively esoteric & pedantic subject, but if you have any thoughts on the matter, I'd certainly appreciate it.

For example, ignoring the hoop tension forces created by the bullet's jacket that resist expansion for the time being, a 9mm 147-grain JHP made of 2% antimonial lead, would have a yield strength of 3,480 psi (24.0 MPa)

Forgive me, I am poorly versed in engineering matters - would you know how low this can go and/or whether the size and shape of a hollowpoint influences this?

I was wondering because Federal has apparently stated that the 230 gr HST is capable of expansion at velocities down to 700 FPS. Presumably when they are saying this, they mean that the bullet can actually achieve a meaningfully expanded state, which in turn would mean the minimum deformation velocity is probably significantly lower than 700 FPS.

I hate to reference any clear gel data but we do know the approximate density of this material (~790 kg/m³) and we have a demonstration that a 230 gr HST traveling at ~825 FPS can expand to about 0.71" in this material after passing through 4 layers of denim. If the yield strength of the bullet were the same as the example 147 gr, it would appear, using the modified Bernoulli equation for 790 kg/m³ media:

√[(2 x 24,000,000 N/m²) ÷ 790 kg/m³] = 246.5 meters/second, or about 808.7 FPS.

It seems virtually impossible that a bullet could expand from 0.45" to 0.71" after slowing down by only 16 FPS. However, I am not sure if there are other variables that make this equation inapplicable. From what I know, total penetration and expansion figures with clear gel are almost impossible to scale to ordnance gel because the density is considerably lower and the shear resistance is considerably higher (resulting in increasing total resistance at low velocities and decreasing total resistance at high velocities, with an arbitrary break-even point); but for trying to calculate the minimum expansion velocity using Bernoulli's equation, I'd guess shear resistance wouldn't be meaningfully relevant at ~800 FPS, and density is naturally one of the independent variables.

Assuming though that the actual minimum fps threshold for a 0.79 g/cm³ material were 700 FPS (I haven't done any calculations for this so I realize this estimate has little precise basis, it could just be called a vague postulate for the sake of speculation), this would seemingly imply a 18,000,000 N/m².

It seems like this is quite a substantial decrease, but it appears to be roughly consistent with Federal's claim in ordnance gelatin/actual flesh:

√[(2 x 18,000,000 N/m²) ÷ 1040 kg/m³] = 186.1 meters/second, translating to roughly 610 FPS.

A window of 700 FPS to 610 FPS seems like it might be enough to produce the deformation necessary to credibly call a bullet 'expanded'.

My apologies if this is a complete perversion of the maths required, I'm not very familiar with the physics side of the topic.

[HCM]

So shoot them as they exhale.

I don’t remember that in the movie ..

[the Schwartz]

Thank you for taking the time to help me out.

I assume in most cases that the average density of a living attacker's lungs will be closer to the inflated figure since they will naturally contain some air even when breathing out. However, it seems like the bullet would compress tissue while moving forward - this should, at least theoretically, result in the creation of a mass of flesh in the hollowpoint cavity and/or just in front of the bullet that is denser than the medium itself.

In other words, the bullet may be "deflating" the lung tissue right in front of it. Exactly how much and to what extent is the part that I don't know.

Could this be relevant?

Doubtful. Respiratory cycles for adults range from 12 to 18 breaths per minute ranging in duration from 3 to 5 seconds. A bullet passing through pulmonary tissue at ≈700 fps does not have the ability accelerate the process of deflation since it passes through a 6'' wide lung in about 0.7 milliseconds.

I suppose this depends on 1) how quickly any crushed tissue gets shucked off to the side rather than remaining in front of the bullet, 2) how much pressure the bullet exerts on tissue ahead of it that it has no directly contacted yet, 3) whether there is any difference in its ability to compress inflated lung vs deflated lung or muscle.

If there is no difference in #3 then the required expansion velocity in inflated lung should follow normal calcs if the required expansion velocity in deflated lung/muscle is roughly known. However it seems like there could plausibly be some substantial difference since an air-filled mass of elastic tissue seems inherently more compressible than the same elastic tissues that don't contain significant quantities of air; after all, its ability to change volume/collapse easily is part of why lung density can vary so much in the first place.

Under dynamic compression, the initial bulk modulus (a measure of compressibility) of the pulmonary tissue may change subtly, but not enough to matter in any significant way.

Forgive me, I am poorly versed in engineering matters - would you know how low this can go and/or whether the size and shape of a hollowpoint influences this?

That would depend upon the geometry of the expansion cavity.

I was wondering because Federal has apparently stated that the 230 gr HST is capable of expansion at velocities down to 700 FPS. Presumably when they are saying this, they mean that the bullet can actually achieve a meaningfully expanded state, which in turn would mean the minimum deformation velocity is probably significantly lower than 700 FPS.

The Federal HST is a solid, well-engineered design. If that's the number they give, I'd take Federal at their word as to the bottom of the range.

Assuming though that the actual minimum fps threshold for a 0.79 g/cm³ material were 700 FPS (I haven't done any calculations for this so I realize this estimate has little precise basis, it could just be called a vague postulate for the sake of speculation), this would seemingly imply a 18,000,000 N/m².

Since Federal conducted the development of the HST using the industry standard 10% ordnance gelatin, it is only reasonable to mathematically ''reverse-engineer'' the correct yield strength for the Federal HST @ 700 fps (213.4 m/s) using the density of 10% gelatin. The clear gel stuff doesn't tell us anything of value. I have never asked Federal what alloy they use to manufacture the HST. I imagine that they'd be rather tight-lipped about it being proprietary information and all that.

In that case, the correct yield strength of the (unknown) Federal HST alloy would be = ½ x 1,040 kg/m³ x (213.4 m/s)² = 23.7 MPa, not 18.0 MPa

A yield strength of 18 MPa would indicate an unusually low percentage (≈½%) of antimony in the core alloy.

Domestically produced JHPs typically use lead-antimony alloys in the 2% - 3% range.

[GhostCan]

Doubtful. Respiratory cycles for adults range from 12 to 18 breaths per minute ranging in duration from 3 to 5 seconds. A bullet passing through pulmonary tissue at ≈700 fps does not have the ability accelerate the process of deflation since it passes through a 6'' wide lung in about 0.7 milliseconds.

I suppose referring to any such phenomenon as true deflation would not technically be correct - rather speaking of "squishing" tissue immediately ahead of the bullet that may or may not involve any real outletting of air. The talk of deflating is simply a way to simplify and 'visualize' the conversion of less dense lung tissue to more lung tissue, in connection with the density figures for inflated and deflated lungs, for any readers that might be lost from trying to decipher my perhaps confusingly wordy talk. I realize from a medical/physiological perspective, such a descriptor is perhaps nonsensical.

Under dynamic compression, the initial bulk modulus (a measure of compressibility) of the pulmonary tissue may change subtly, but not enough to matter in any significant way.

Do you think this would still apply for the tissue that is "packed" into a hollowpoint cavity? Intuitively it seems like it would continually squash into a limited space as the bullet continues to penetrate, unless the bullet has expanded well enough already that the leading surface of the bullet has become largely flat and no real concave cavity exists anymore.

I am curious because, from my impression (correct me if I am wrong), lung density is only really very close to its deflated figure when the lung is fully collapsed, i.e. subject is probably dead or pretty close to it. The fully inflated figure would be presumably applicable in cases where a person takes the largest breath possible; not really doable without trying, but possibly closer to the normal state of the lungs than fully collapsed. It seems like, if lung density is usually close to the fully inflated figure, most handgun bullets will be hard pressed to expand in this medium. However I also do not know the "minimal" density of the lung that can be expected under DGU circumstances.

There are some figures for normal air volume of the lung vs total capacity of the lung which seem to suggest that normal volume is about half of total capacity. Assuming this means "average" lung density is about halfway in between inflated lung density and deflated lung density, at about 0.73 g/cm³, this certainly seems capable of facilitating bullet expansion in some rounds. Unfortunately I don't know how closely the current air capacity of a lung correlates with its actual spatial volume, given the compressibility of air and the amount of non-air tissue volume. That is, if the lungs have a maximum capacity of 6 L of air (presumably this would be the "completely inflated" scenario) and they instantaneously hold up to about 5 L of air (conjectural figure) in a gunfight, how much does the physical volume and density of the lungs, change from 6 L air volume to 5 L air volume? Is it 5/6 of the way between 1.05 g/cm³ and 0.4 g/cm³? If they "average" 4 L, what does the average lung density become? Is it 4/6 of the way between 1.05 g/cm³ and 0.4 g cm³.

You are certainly not obligated to continue answering these questions if they are annoying you, but I do enjoy learning about the topic and the insights you provide. Please know that I appreciate your work and am not just trying to pester you.

Since Federal conducted the development of the HST using the industry standard 10% ordnance gelatin, it is only reasonable to mathematically ''reverse-engineer'' the correct yield strength for the Federal HST @ 700 fps (213.4 m/s) using the density of 10% gelatin. The clear gel stuff doesn't tell us anything of value. I have never asked Federal what alloy they use to manufacture the HST. I imagine that they'd be rather tight-lipped about it being proprietary information and all that.

In that case, the correct yield strength of the (unknown) Federal HST alloy would be = ½ x 1,040 kg/m³ x (213.4 m/s)² = 23.7 MPa, not 18.0 MPa

A yield strength of 18 MPa would indicate an unusually low percentage (≈½%) of antimony in the core alloy.

Domestically produced JHPs typically use lead-antimony alloys in the 2% - 3% range.

The caveat is that Federal apparently claims 700 FPS is the velocity at which the bullet will expand, rather than the minimum speed at which the lead can deform. In this context, expansion can probably be interpreted to mean "increases in diameter noticeably". If I am correct, a bullet with a minimum deformation velocity of 700 FPS will basically not expand at all, since it will instantly drop below 700 FPS upon contact.

However, at ~18.0 MPa (again, a very speculative wild guess), the bullet starts expanding at 700 FPS (impact velocity) and continues expanding until it slows down to about 610 FPS. It seems like this would be enough time spent expanding for the bullet to be counted as "expanded" to an observer.