Statistical Analysis of "Energy Transfer"
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MrAcheson
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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.
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
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How are you calculating momentum for these charts?
MrAcheson
Member
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.
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.
( 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
Member
Or you could just use the IPSC "power factor" and go with grains*fps/1000. This is a momentum measure too.
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.
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.
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?
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
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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.
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
member
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.
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.
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.
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.
Pretty good correlation I'd say.
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.
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.
Pretty good correlation I'd say.
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Michael Courtney
Member
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
In defense of Mr. Courtney
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
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
Member
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.
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,
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
Member
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
Member
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.
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.
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.
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
Member
Interesting and it sounds like you have things well in hand. Thanks for the reply.
trapperjohn
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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?
what made you choose that over surface area or depth of penetration?
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