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Bullet penetration, pt 2.
beantownshootah
Member Posts: 12,776 ✭✭✭
Continuing the previous thread on this:
quote:heavyiron
Momentum does not explain the difference in penetration in this case either, since momentum (Mo = M x V) for both projectiles is approximately equal due to the velocity difference. The difference in kinetic energy is much greater than the difference in momentum which again is about equal. Remember the equations use mass not bullet weights even though bullet weight is used to calculate the mass.
First of all, grains actually are a unit of mass, not weight. Grains are currently defined (by mass) in the international yard and pound agreement of 1959 as 64.79891 milligrams.
Yes, technically weight is mass x the force of gravity, but since gravity is a constant, for practical discussion of bullets travelling at the surface of the earth mass and weight are functionally equivalent.
With respect to momentum, you may wish to re-check your arithmetic. Repeating what I said in the last thread, if you have two projectiles with equal kinetic energy, the one with higher MASS will have higher MOMENTUM. Here's the comparison again, with actual published ballistic data, only this time including calculated momentums to assist in comparison:
Winchester 62 grain .223 @ 3100fps; 1323 ft-lbs kinetic energy; 0.8534 pound-force seconds momentum.
Winchester 123 grain 7.62x39 @ 2355 fps; 1515 ft-lbs kinetic energy; 1.286 lb-force seconds momentum.
Of course you can tweak the individual loads a little bit, but these are standard loads, and with them, the 7.62x39 offers roughly 15% more kinetic energy, and fully 50% more momentum (ie "power factor"). So purely based on external ballistics, you'd expect the 7.62x39 to offer roughly 50% more "knockdown" power.
Again, although kinetic energy, and especially momentum are typically OK approximations of wounding potential, there are other factors in play including bullet design. Again, in practice, the slower fatter FMJ 7.62x39 rounds tend to hold together after impact, where as the .223 rounds are travelling literally near Mach 3, and not only provide significant hydrostatic shock effect, but because of the velocity, they also tend to fragment on impact, potentially causing disproportionate tissue damage. This is part of the reason why the Soviet Bloc countries largely switched from 7.62x39 to 5.45x39. You can significantly improve the terminal performance of 7.62x39 by switching to a non-standard bullet design, but bullets designed to expand are specifically prohibited by the Hague ("Geneva") convention, and aren't perimissible for use in wartime by signatory nations.
quote:heavyiron
Momentum does not explain the difference in penetration in this case either, since momentum (Mo = M x V) for both projectiles is approximately equal due to the velocity difference. The difference in kinetic energy is much greater than the difference in momentum which again is about equal. Remember the equations use mass not bullet weights even though bullet weight is used to calculate the mass.
First of all, grains actually are a unit of mass, not weight. Grains are currently defined (by mass) in the international yard and pound agreement of 1959 as 64.79891 milligrams.
Yes, technically weight is mass x the force of gravity, but since gravity is a constant, for practical discussion of bullets travelling at the surface of the earth mass and weight are functionally equivalent.
With respect to momentum, you may wish to re-check your arithmetic. Repeating what I said in the last thread, if you have two projectiles with equal kinetic energy, the one with higher MASS will have higher MOMENTUM. Here's the comparison again, with actual published ballistic data, only this time including calculated momentums to assist in comparison:
Winchester 62 grain .223 @ 3100fps; 1323 ft-lbs kinetic energy; 0.8534 pound-force seconds momentum.
Winchester 123 grain 7.62x39 @ 2355 fps; 1515 ft-lbs kinetic energy; 1.286 lb-force seconds momentum.
Of course you can tweak the individual loads a little bit, but these are standard loads, and with them, the 7.62x39 offers roughly 15% more kinetic energy, and fully 50% more momentum (ie "power factor"). So purely based on external ballistics, you'd expect the 7.62x39 to offer roughly 50% more "knockdown" power.
Again, although kinetic energy, and especially momentum are typically OK approximations of wounding potential, there are other factors in play including bullet design. Again, in practice, the slower fatter FMJ 7.62x39 rounds tend to hold together after impact, where as the .223 rounds are travelling literally near Mach 3, and not only provide significant hydrostatic shock effect, but because of the velocity, they also tend to fragment on impact, potentially causing disproportionate tissue damage. This is part of the reason why the Soviet Bloc countries largely switched from 7.62x39 to 5.45x39. You can significantly improve the terminal performance of 7.62x39 by switching to a non-standard bullet design, but bullets designed to expand are specifically prohibited by the Hague ("Geneva") convention, and aren't perimissible for use in wartime by signatory nations.
Comments
1.Frontal area and shape of bullet(at each instant of contact)
2.Amount of push on the bullet
3.Resistance given by the penetrate.
#1 changes either by the bullet changing shape or by turning sideways.
For most practical applications weight and mass are synonymous. Most people and even some engineers and scientists use these terms interchangeably. In most cases, the interchangeable use of weight and mass in mathematics is acceptable. Two 100 grain bullets will have a total mass of 200 grains. Fine. Nobody normal really needs to worry about it.
However, scientists and engineers do discriminate between mass and weight because there are technically valid reasons to do so. To assume weight and mass are equivalent for Newton's Laws of Motion is is a mistake.
Weight refers to a force experienced by an object due to gravity. One difference between weight and mass is, weight will vary by location. An example is 6 pounds of lead on earth will only weigh 1 pound on the moon because the moon's gravity is approximately 1/6 that of the earth. That same 6 pounds of lead will weigh more than 6 pounds on the sun because there is more gravity on the sun and the lead will be almost weightless in space.
Mass refers loosely to the amount of "matter" in an object, though "matter" may be difficult to define. Another difference between weight and mass is that mass will have the same mass, no matter where it is located in the universe, albeit the moon, the sun, or in space the mass will remain unchanged. There are other differences but those aren't our concern here. The references below will go into greater detail and will document this important point:
http://www.diffen.com/difference/Mass_vs_Weight
http://en.wikipedia.org/wiki/Mass_versus_weight
BTS (Beantownshooter) stated: "First of all, grains actually are a unit of mass, not weight" and "for practical discussion of bullets travelling at the surface of the earth mass and weight are functionally equivalent." He then goes on to state: "With respect to momentum, you may wish to re-check your arithmetic."
As an example, assume weight and mass are the same as BTS says they are and are interchangeable units. Using the above assumption, Newton's Second Law will now be used to calculate momentum from Newton's formula:
M = (mb/CF) x vb Equation 1
Where:
M = Momentum in pounds force second (lbf s)
mb = mass of bullet 123 grains (grns)
CF = Conversion Factor = 1 lb/7000 grns since the result is in pounds and not grains
vb = velocity of bullet 2355 feet per second (fps)
BTS stated grains are mass so the 7.62 x 39 - 123 grain bullet and its velocity of 2355 fps, can be substituted directly into the formula:
M = (123 grns/7000 grns) x 2355 fps
M = 0.017571 x 2355
M = 41.38 lbf s
Uh-Oh. BST's result from a published source was 1.286 lbf s so something is wrong.
What if the assumption that weight and mass are equivalent was wrong and the weight and mass really do need to be converted to a mass? Maybe grains really are weight and if the weight was converted to a mass the formula might still work. We can do that thanks to Newton's Second Law. Newton says that weight can be converted to mass using the following formula:
m = Wb/7000/g Equation 2
Where:
m = Mass in pounds (lb)
Wb = Bullet weight in grains (grns)
g = Acceleration due to gravity is 32.2 feet per second squared (32.2 ft/s^2)
By combining both Equations 1 and 2 and substituting the appropriate parameters the equation is:
M = (123 grns/7000 grns/32.2 f/s^2) x 2355 fps Equation 3
M = 0.0005457 x 2355
M = 1.285 lbf s
It worked! My math is checked and it is the same as that BTS found in his publication for momentum for a 7.62 x 39. BTS's book value indicated the momentum was 1.286 pounds and my arithmetic calculated 1.285 pounds. Close enough since it didn't say how his publication had calculated momentum and since both momenta are identical for all practical reasons my math is OK.
It was also proven mathematically that weight and mass are not functionally equivalent for Newton's Laws. Weight does not work in Newton's equations - weight must be converted to mass in order to obtain the correct result.
BTS then states "Repeating what I said in the last thread, if you have two projectiles with equal kinetic energy, the one with higher MASS will have higher MOMENTUM."
My response to this statement is "So What - It's not important". The two projectiles are so close in performance it is like splitting hairs as to which one provides greater momentum. If this is the case it won't matter because there will be no observable or measurable difference in the real world. The difference in momentum could be calculated but it will be so small it will not make the least bit of difference.
Okay so let's take about momentum. Assuming the gun and shooter are at rest, the force on the bullet is equal to that on the gun-shooter. This is attributable to Newton's Third Law which states that for every action there is an equal and opposite reaction. Consider a situation where the gun-shooter have a combined mass M and the bullet has a mass mb. When the gun is fired the gun/shooter and bullet move away from one another at velocities called (V shooter/gun) and (vb bullet)due to the opposing forces. However, the law of conservation of momentum states the amount of their momentum must be an equal force, that is an equal force on the shooter/gun and an equal force on the projectile. In equation form it is expressed as:
M x V + mb x vb = 0
This means the force equals the rate of change in momentum and the initial momenta are zero. In other words the force on the bullet must therefore be the same as the force on the gun/shooter! Therefore, the bullet has no more momentum than the recoil of the firearm and shooter because the two forces have to be opposite and equal. If the momentum is powerful enough to stop the target, then the recoil has to be powerful enough to stop the shooter as well.
Everyone remembers a western movie where a bad guy is shot by both barrels of a double barrel shotgun and goes flying for many feet through the air or is blown out of a saloon window breaking a window on his journey through the air. This is pure garbage and tinsel town drama. This situation does not exist in real life with pistols or shoulder fired rifles or shotguns. If the bad guy is hurled backwards for several feet by the momentum of the projectile, the good guy with the shotgun will also be thrown backwards an approximately equal distance. So there is no huge delivery of energy from the momentum of a project when it impacts. It is in balance with the shooter and his weapon.
Here is a formula to help calculate how far momentum would move a 170 lb target caused by the momentum of projectile impact.
Assume a 123 grn bullet with a bullet velocity of 2355 fps and a 170 lb target. The formula is:
Wb x vb = Wt x Vt
Vt = Velocity of target fps
vb = Velocity of bullet 2355 fps
Wt = Weight of target 170 lbs
Wb = Weight of bullet 123 grns
(123grn/7000grn) x 2355 fps = (170 lb) x Vt
0.017571/7000 x 2355 = 170 x Vt
Vt = 0.2434 fps
This example shows the target barely moves 3 inches from the 7.62 x 39 projectile. Therefore, momentum cannot be a major force. The momenta published above are miniscule quantities - they are puny as far as force is concerned. The 5.56 Nato provides only 0.8534 pounds force of momentum and the 7.62 x 39 provides only 1.28 pounds force of momentum (even though it is 50%) greater than the 5.56 Nato. My opinion is 50% greater than almost nothing is still almost nothing. Our cat jumping on our lap provides more momentum than 1 pound of force.
The smaller mass of the bullet compared to that of the gun-shooter allows significantly more kinetic energy to be carried by the bullet to the target. Because the mass of the bullet is much less than that of the shooter/firearm, there has to be more kinetic energy transferred to the bullet and to the target.
People in ballistic vests don't often have the panels penetrated by projectiles. The projectile is slowed by the material and the kinetic energy is dissipated over a larger area of the vest to reduce the impact. However, people are hurt and killed in ballistic vests without projectile penetration because of the kinetic energy causing blunt force trauma to the vital organs and bones.
This is the proof and basis for my statements. The kinetic energy of the cartridges under study are much more powerful than the momentum from any of the projectiles. The kinetic energy of the 5.56 Nato is 1323 ft-lbs and the 7.62 x 39 has 1515 ft-lbs of kinetic energy. The energy of both cartridges dwarfs their momentum of 0.8534 pounds for the 5.56 Nato and the 1.28 pounds momentum for the 7.62 x 39 cartridge. The force of momentum is limited since it cannot exceed the momentum of the recoil from the gun-shooter system.
Momentum is not stopping power. There are adherents of the momentum theory but there is serious disagreement regarding its validity. Certainly, larger caliber weapons with a heavier projectile and higher velocity would generate greater momentum than the two cartridges under study here. But momenta for both the 5.56 Nato and the 7.62 x39 are relatively weak and cannot be considered an important factor in bullet penetration.
Best,
Heavyiron
For most practical applications weight and mass are synonymous.Yes, and since this is true for the specific discussion of comparing bullet ballistic performance, I'm not addressing this distinction further.
quote:As an example, assume weight and mass are the same as BTS says they are and are interchangeable units. Please stop misquoting me. Not only did I NOT say they were the same, in fact, I specifically defined the difference between the two, above. What I said was that the two are functionally equivalent for purposes of comparing ballistics, and I stand by that. Even if you were to wrongly substitute weight for mass in calculating momentum or energies (which I did NOT) so long as you did this consistently the proportion between your answers would be the same and the comparison between rounds would still be valid.
More simply, whether you use mass OR weight to do your calculation, 7.62x39 still offers 15% more energy and 50% more momentum than .223. Despite your lengthy post, you still haven't refuted this.
quote:BTS then states "Repeating what I said in the last thread, if you have two projectiles with equal kinetic energy, the one with higher MASS will have higher MOMENTUM."
My response to this statement is "So What - It's not important". The two projectiles are so close in performance it is like splitting hairs as to which one provides greater momentum.
You have this exactly backwards. We know, that .223 and 7.62x39 DO NOT offer the same performance, which is sort of the whole point of this thread. . .if they have similar energies, why do they perform differently?
Momentum is a directly measurable quantity. . .no "hair splitting" is necessary to measure it. On momentum itself, it DOES matter, and while of course other factors also matter, many authorities consider it to be the single biggest individual factor in conventional "stopping power", in particular, more important than the usually cited kinetic energy. For example "taylor knockdown power" and IPSC-type "power factor" are both basically just products of momentum.
As one relevant example most shooters are familiar with, both standard ball 9mm luger and .45ACP ammo each yield about 350 ft-lbs of energy. But the .45ACP offers higher momentum, and not coincidentally, the 45 is widely considered to have greater knockdown power. Are you saying the difference here is "not important"?
As another example, a 40 grain 22-250 bullet will get 4150fps at the muzzle, yielding 1529 ft-lbs of energy. For comparison, a 250 grain .454 Casull magnum handgun round will get about 1650fps muzzle velocity for a nearly identical 1514 ft-lbs of energy. But while the two energies are equivalent. . .the .454 offers 2.5x as much momentum and WAY more penetration.
Are you saying these two rounds are equivalent? Which one do you think is better for hunting an elk? How about which one do you want in your hands if charged by a Grizzly bear? The difference in PENETRATION between these two (and that's what this post is about) is "not important"? I certainly hope you don't actually believe this.
quote:This is the proof and basis for my statements. The kinetic energy of the cartridges under study are much more powerful than the momentum from any of the projectiles. The kinetic energy of the 5.56 Nato is 1323 ft-lbs and the 7.62 x 39 has 1515 ft-lbs of kinetic energy. The energy of both cartridges dwarfs their momentum of 0.8534 pounds for the 5.56 Nato and the 1.28 pounds momentum for the 7.62 x 39 cartridge. The force of momentum is limited since it cannot exceed the momentum of the recoil from the gun-shooter system.This is silly-talk. You're comparing apples and oranges. Kinetic energy and momentum are partly related, but they're DIFFERENT THINGS, and they are measured using different units (which, by the way, you could at least try to get right since you're making a big show of this post). That's why in absolute terms the KE numbers dwarf the momentum numbers. . .the units of measurement are different. . .not because one is "more" than the other!
In effect, what you're saying is that the impact of a 1 ton weight falling on your head is less than that of a 15 ounce grapefruit, because 15 is a much bigger number than 1!
quote:Momentum is not stopping power. There are adherents of the momentum theory but there is serious disagreement regarding its validity. Momentum is ONE potential measure of stopping power, but obviously there is quite a bit more to it than that. I already mentioned bullet construction and hydrostatic shock as two other relevant factors, above.
Probably the single best use of momentum as a partial surrogate for stopping power is "Taylor knockdown power" which is a VERY specific application looking at performance of large caliber SOLID bullets in heavy/dangerous game. The calculation, IIRC, involves the product of momentum and bullet cross sectional area. But obviously shooting Rhinos and people are different things.
quote:But momenta for both the 5.56 Nato and the 7.62 x39 are relatively weak and cannot be considered an important factor in bullet penetration.On what basis do you come to this conclusion? Because the absolute numbers in pound-force seconds are low?
7.62x39 is a low-medium power centerfire rifle round, roughly on a par with a 30/30 rifle round. True, compared to "bigger" rifle rounds it doesn't offer all that much momentum, but I don't think anyone on the receiving end of one of these to their head is going to think the momentum isn't "important"!
In effect, what you're saying is that the impact of a 1 ton weight falling on your head is less than that of a 15 ounce grapefruit, because 15 is a much bigger number than 1!
This is one of the best summaries of a long-winded post I have read in a long time.
Well played, sir.[:)]
Brad Steele
...actually, even though I'm woefully under educated in physics (my own fault, I failed to pay attention when the instructors tried to teach me), I do find this to be a very interesting discussion. I've learned more from reading/re-reading this thread than I did in most of my physics classes.
I'll make this REALLY simple.
If you want to compare projectiles, if you have two different ones with similar kinetic energies, the one with more momentum will have more "stopping power". More succinctly, slower heavier bullets generally tend to offer better penetration, and better stopping power than faster lighter ones with similar energies.
Some people use the term "knockdown power" as synonymous with "stopping power", though I didn't and technically speaking, they're not exactly the same thing. The ability of one object (eg a projectile) to knock down a second one, is directly attributable to its momentum.
When I said that a bullet with 50% more momentum will have 50% more "knockdown" power, I meant it literally. . .the bullet would offer a much better chance of knocking over a steel plate, for example. In this specific case, the original question was why does a 7.62x39 crack a cinder block when a similar energy .223 doesn't? Same thing. . .in this case, the heavier projectile with similar energy offers significantly more momentum. .
As heavyiron said above in a roundabout way, no small arms projectile really has a lot of "knockdown power" in an absolute sense, otherwise it would knock over the shooter from recoil. Contrary to what is depicted in bad Hollywood movies, in the real world human beings don't get knocked off their feet by the impact of ordinary pistol or rifle bullets.
Still, as a first approximation, "knockdown power" is directly proportionate to momentum, which is also correlated with bullet weight and (to a lesser extent) stopping power.
While stopping power and momentum aren't exactly synonymous, in practice, they tend to be related, just as kinetic energy and stopping power are also related, albeit imperfectly.
Hope that helped.
Momentum and force are different things measured in different units. Momentum is not a force.
That's why statements like this don't make sense:quote:This example shows the target barely moves 3 inches from the 7.62 x 39 projectile. Therefore, momentum cannot be a major force. The momenta published above are miniscule quantities - they are puny as far as force is concerned. The 5.56 Nato provides only 0.8534 pounds force of momentum and the 7.62 x 39 provides only 1.28 pounds force of momentum (even though it is 50%) greater than the 5.56 Nato. My opinion is 50% greater than almost nothing is still almost nothing. Our cat jumping on our lap provides more momentum than 1 pound of force. First of all, the thing quoted in red above is risible. How can you claim with a straight face that your calculation shows a movement of "3 inches" of the target when none of the calculations are even done using inches as units of measurements? Where did that number come from?
The fact is, with the information you provided there is absolutely no way for you or anyone else to possibly determine how far a target will move in recoil, because the primary determinant there is FRICTION, something that you didn't even mention in your calculations, let alone model.
If your target were in a theoretical zero friction environment (eg space), it would move an INFINITE distance after being struck by a bullet because of Newton's first law. As a more practical example, if your target were on wheels, it would move further than if it were sitting on sand, and if it were on ice, it would move further yet.
As to the cat example, again, a pound of force is NOT the same thing as a pound-force/second of momentum, and you can't directly compare the two.
For an easy illustration comparing your cat to a gun, a loaded SKS rifle with sling weighs about 9 lbs (so that's 63000 grains). For simplicity, lets say your cat also weighs about 9 lbs. Using conservation of momentum, a 123 grain 7.62x39 leaving the muzzle at 2355 fps will cause a 63000 grain rifle to recoil at about 4.6 feet/second velocity.
An object falling 6 inches at sea level will reach a final velocity of about 5.6 ft/sec.
You can tweak the numbers further, but at a first approximation, assuming your cat jumps right onto your lap, its momentum hitting your lap will be roughly the same as that of a 7.62x39 rifle round.
But again since momentum is NOT force, this particular comparison isn't very meaningful.
Even though on impact your jumping cat may very well move your body roughly the same amount as the recoil from the SKS rifle, that's not really the most important thing to consider here! Your cat has soft feet, your lap is soft, and your couch is soft. So the force exerted by the cat onto your lap is cushioned three different ways and spread out over both time and area. You can be fairly well assured that with identical momentum to your cat. . .or even quite a bit LESS momentum. . .a 7.62x39 rifle round hitting you in the groin is going be a "little" more unpleasant than the cat jump!
quote:Ray B
the difference is Weight is a force, ie the mass is pushing, in the case of gravity, down; whereas Mass is just an amount of stuff with no acceleration.
This is correct. Weight is the force exerted on a object by gravity; mass is the way one typically quantifies the amount of matter in an object. Confusing this quite a bit, the term "pound" technically is a unit of weight, but its also commonly used a unit of mass. This potential confusion is one reason why physicists almost invariably prefer to measure things using less ambiguous SI units.
Technically, the unit of MASS in the US common system is a "slug". A slug. . .which has a WEIGHT of 32.2 pounds. . .is the amount of mass one pound of force will accelerate to exactly 1 foot/second^2. But in practice, virtually nobody uses this unit. . .a 32 pound "thing" isn't very practical for commerce or every day transactions, and again, since mass and weight are for *practical* purposes synonymous at sea level, there is little need for this unit outside of rarefied physics discussions.
The only thing that 'stops/kills'(a live target)is a deep, wide wound cavity (blood lose). ALL of the sciences have a role in terminal ballistics.
That said, all things being equal the projectile with the highest momentum (if the bullet retains it's weight) will penetrate further. The size of the wound cavity is the determining issue in the ability to 'stop' the target, and penetration to the 'vitals' is a requirement in this endeavor.[:)]
http://www.chuckhawks.com/rifle_killing_power.htm
"Linear momentum
Momentum is calculated differently from energy in that it is the product of mass and velocity--not the square of velocity. This slants the result in favor of heavy bullets, and makes momentum the darling of the big bore crowd. Momentum is what tends to keep a mass in motion moving, in accordance with one of Newton's physical laws. It is unclear how (or if) this relates to killing power.
Momentum is not widely referred to in the world of ballistics (terminal or otherwise). The term "momentum" is not even included in the Glossary of Terms in the back of the Hodgdon, Hornady, Lyman, Nosler, or Speer reloading manuals that happen to be piled on my desk as I write these words. (I checked!) I am inclined to conclude that momentum is a sort of red herring, favored by gun writers from the big bore school because it gives credibility to their existing prejudices in favor of big bore rifles and heavy bullets.
The term "pounds feet" invented, I believe, by Elmer Keith, is another favorite comparative tool of the big bore school of gun writers. Pounds feet is merely momentum divided by 7000 (the number of grains in a pound). The comparative result is the same as an ordinary calculation of momentum, but using the term pounds feet gives the result a sort of pseudo scientific ring, as the lay reader may easily confuse "pounds feet" with the legitimate scientific measurement "foot pounds."
As we have already seen, large diameter bullets tend to create a wide wound channel, and bullets that are heavy for their caliber have good sectional density and tend to create deep wound channels other factors being equal. These are clear advantages of heavy, large bore bullets from the standpoint of killing power. However, I doubt that calculating bullet momentum per se contributes anything to our understanding of the subject. Ditto for pounds feet.
Another of Sir Isaac Newton's physical laws states that for every action there is an equal and opposite reaction, calculated in terms of momentum. This would imply that, in terms of momentum, the recoiling rifle has more killing power than the bullet it fires, since its momentum is in fact the same as the total ejecta from the barrel (the bullet plus the powder gasses). It is true that big bore rifles kick like the devil, but I doubt that even the most fervent true believer wishes to defend momentum as an indication of killing power in that light, for if it were true they should all be dead."