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Momentum vs Kinetic Energy visualized, no mention of lethality

Discussion in 'General Gun Discussions' started by mcb, Nov 22, 2019.

  1. mcb

    mcb Member

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    So playing around try to visualize the four dimensional space that is mass, velocity, momentum, and kinetic energy. This is far from perfect since my four dimensional holograph is on the fritz but after playing around with numbers and Excel for awhile I came up with the following two graphs, one inset in the others and thought I would share and hope it would help someone else's intuition on these four interconnected values often used with projectiles.

    mMZBxaql.jpg
    Click here for full size.

    Hopefully if you click on the link below the image you can see the full resolution version so you can read all the fine print.

    The data for each cartridge is, for simplicity sake, take from SAAMI's publish P&V tables in the front of the Pistol and Revolver volume and the Rifle Volume. The other odd ball projectiles are taken from googling the needed data. For each cartridge I took a bullet of weight I thought most representative of the cartridge, this was usually a slightly heavy for caliber but rarely the heaviest of those show in the table. No doubt some of these cartridges are common loaded to higher performance than the SAAMI table but these are based on standard ammo and I thought the fairest representation for each cartridge.

    The inset graph is for showing what mass vs velocity is used to calculate the momentum and kinetic energy in the larger graph for each projectile. The horizontal axis in the inset graph is logarithmic.** This spread things out better so you can actually read all the cartridge names.

    On the main graph the vertical axis (kinetic energy) is likewise plotted on a logarithmic** scale this was done so you could actually see the pistol cartridges that otherwise all ended up in a little messy cluster in the bottom left corner of the graph otherwise.

    The dotted lines on the main graph represent constant mass (red) and constant velocity (black) lines. If you move back and forth along a constant velocity line you are increasing or decreasing mass, conversely if you move along a constant mass line you are increasing or decreasing velocity. If the vertical axis was not logarithmic the black constant velocity lines would be straight lines and the red constant mass lines would be parabolas as expected.

    Sorry if your favorite cartridge is not there, I tried to pick relatively mainstream cartridges. If there is interest I might add more data to the graph. The odd-ball projectiles like the Nerf dart and baseball are there to try to help add some more intuition to this endeavor. Along with other cartridge I would love to add some other non-bullet projectiles to the graph to help with that intuition. Suggest away.

    Any mistakes, though unlikely :D, feel free to point out and I will do my best to correct.

    I am sure some will want to jump into a lethality discussion and that's fine but be prepare for me to say that its not that simple. This post was not intended to make any assertions with regard to lethality but to simple visualize the relationship between mass, velocity, momentum (P=mv), and kinetic energy (E = 0.5mv^2).

    **If you not familiar with logarithmic scales each minor line between the labeled major lines is a multiple of the left line. The third line over from 10 is 40, the fifth line over from 100 is 600.
     
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  2. lysanderxiii

    lysanderxiii Member

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    Just another data point showing momentum and energy are poor parameters to define lethality...

    An NFL linebacker hitting a free running receiver unleashes about 6,000 foot-pounds of energy and has a combined momentum change of 500 to 600 slug-ft/sec. And, not only does nobody die, they do it about twenty times over the course of a Sunday game.
     
  3. mcb

    mcb Member

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    It ain't that simple, the kinetic energy is the only source of energy a projectile has to do anything at the target and momentum has to be conserved as we dissipate the energy into its many other forms (some useful, some not) as a result of the collision. The football player collisions are spread-out over huge areas of the bodies involved in the collision, bodies which are armored with semi ridge plates back by padding over a larger portion. A projectile like a bullet concentrates that energy/momentum over a much smaller areas. The football player collision rarely concentrate the energy/momentum into a small enough area to generate stresses that exceed the local yield stress of the material involved in these larger surface area collisions. The projectile on the other hand easily generates stresses that exceed the yield strength of the material involved and damage occurs.

    These two numbers, kinetic energy and momentum, are critical and inseparable quantities that control a collision but insufficient in the absent of other information to predict the outcome.
     
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  4. murf

    murf Member

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    contact area is going to be a toughie!

    murf
     
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  5. Steve S.

    Steve S. Member

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    Interesting visual mathematics; depicts what most experienced shooters know but cannot elaborate in such detail - very grand intellectual detail. In my much simpler world, my .308 150 grain SST is still needing a deer desiring suicide to walk into it’s path - very slow season for me - I will try again this morning.
     
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  6. jmr40

    jmr40 Member

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    Momentum is useful for predicting which load is most effective when it comes to knocking down steel plates, bowling pins, or other objects. It is completely irrelevant as to bullet performance on living beings.

    Energy numbers can be used to predict bullet performance, but not energy alone. There are other factors to consider such as bullet construction. If bullet construction is similar, and if the bullets are impacting within the velocity range they are designed to work in, then energy can be a fairly accurate method to compare different loads. If not then energy numbers can be very misleading. It is possible to have too much energy and create a situation where the bullet is less effective. And some with lower energy numbers will still perform well due to bullet construction.

    The best way to predict bullet performance is to shoot it into ballistic gel. You won't always exactly replicate the penetration you'd get in living flesh. But the bullets that penetrate the best in gel will penetrate best in flesh with identical shot placement. If the bullets impact speed in gel is enough to expand without blowing up in gel, it will work in flesh at that speed.
     
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  7. Kleanbore

    Kleanbore Moderator Staff Member

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    It is indeed!

    Not so fast. Energy is what causes the bullet to deform or expand.

    And while it is energy that does work in cutting or crushing, and momentum that moves things out of the way, in the real world, penetration can correlate to both, depending upon the media, and living beings are not homogenous.

    Which is the better correlation? Doesn't matter.

    If you really want to know, shoot the same undeformable bullet into different media and vary the velocity. See whether the penetration corresponds better to the velocity itself or to the square oof the velocity.

    If the material is reasonably solid and has reasonable shear strength and compression strength, you will likely see better correlation with the square. If elements of the material can be pushed around and aside fairly easily, the answer will be different.

    And if you change sectional density, ogive, or bullet construction or material, all meaningful correlations go out the window.
     
  8. MachIVshooter

    MachIVshooter Member

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    And there is, of course, the time component-the velocity. I hate the term "energy transfer", but it really does describe fairly well what happens when that high velocity body impacts something, creating a shock wave in the medium which an equal energy but low velocity/high mass impact like the football player collision, or, say, a slow moving motor vehicle, do no cause.

    To put it differently, if you affixed a pointy .308" diameter rod to the bottom of a 1.4 ton weight and dropped it from a height of 1 foot, you get the same 2,800 ft lbs of kinetic energy that a .30-06 generates. That rod would absolutely penetrate a human body through-and-through, but will not do nearly the damage that the .30-06 bullet will do even if it does not expand. The rod will pierce some tissue, push others aside, there would be minimal bleeding as the elastic tissues self-seal to a large degree, and it would be a very serious but very survivable wound, even in a vital area. Just a puncture. The .30-06 bullet, on the other hand, is going to crush and tear tissues well beyond what it actually contacts.
     
    Last edited: Nov 23, 2019
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  9. CDW4ME

    CDW4ME Member

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    Get both?
    Underwood 10mm 180 gr. Gold Dot


    In before "doctors can't tell a difference" or "they all perform about the same" :D
     
  10. mcb

    mcb Member

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    Remember one of the points of the above graph is to show that momentum and kinetic energy are inseparable properties of an object in motion. There is nothing you can do to effect one that does not also effect the other property. The dotted lines were included to help see those changes in one dimension, ie if the projectile speeds up or slows down but does not change mass the kinetic energy and moment change along a path parallel with the red lines and if the mass is change up or down while maintaining a constant velocity it changes along the black lines. To say momentum in only good for evaluating X interactions or kinetic energy is only good for evaluating Y interaction is ignoring the fact that you can't have one with out the other.
     
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  11. lysanderxiii

    lysanderxiii Member

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    Duh.

    Momentum = Mass x Velocity

    Energy = 1/2 (Mass x Velocity^2)

    Both only deal with the variables of mass and velocity.
     
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  12. lysanderxiii

    lysanderxiii Member

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    I pointed that out for the sole reason that I hate when people quote muzzle energy as the "proof" that one cartridge, or loading, is superior to another. Terminal ballistics is way too complicated to reduce to one or two figures.
     
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  13. MachIVshooter

    MachIVshooter Member

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    There is some utility in such comparisons among similar cartridges, but one has to take care not to make it an apples and softballs comparison. KE figures betwixt .300 win mag and .300 RUM have some meaning, the more powerful .300 RUM able to drive the same bullet expanded to the same diameter deeper, all else being equal. But if you're talking about a .223 vs. 44 mag, not really useful at all.
     
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  14. mcb

    mcb Member

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    I think the chart above is more useful comparing cartridges like 44 mag & 223 if you willing to look at both values in the context of their caliber and bullet construction. We know despite those two cartridges having similar kinetic energy levls they have very different momentum and reactive very differently in a terminal sense. 44 Mag is going to out penetrate the 223 against soft flesh targets in most cases but against hard targets like steel and even Kevlar/Spectral the 223 will likely out perform the 44 Mag. Similarly a fast-pitch baseball has similar momentum to our 44 Mag but significantly less energy and again we know how dramatically different the terminal effects of both will be both due to the energy difference and the geometry involved.
     
  15. tark

    tark Member

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    The bigger the bullet and the faster it travels.... the more likely it is going to kill something.

    That's all I need to know.......... HOWEVER........ it ain't that simple! A 2,000 gr. bullet from a 4 bore elephant rifle at a velocity of 80 FPS will make major power factor.

    But it won't kill anything.
     
  16. alsaqr

    alsaqr Member

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    Methinks you are correct. i'm a dedicated muzzleloader hunter. A patched .490 round ball with an initial velocity of 1,750 fps has dropped to 1,222 fps at 50 yards, generating 585 foot pounds of energy. At 50 yards that 176 grain ball kills deer as effectively as a .30-06 using a 150 or 180 grain bullet generating 3,000 foot pounds of energy.
     
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  17. 35 Whelen

    35 Whelen Member

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    It blows my mind that in the 21st century there are those that still think they can predict how well a projectile will kill based solely on numbers derived from the weight and velocity of said projectile. Or even those that think energy is what causes a bullet to expand.

    I've killed a fair amount of game with a 35 Whelen. I know for a fact that if I load three 225 gr. bullets, a Sierra SPT, a Nosler Partition and a Barnes TSX, and shoot them into flesh and bone, even though they may have identical bullet energy figures, they all behave differently; penetrating to various depths, making different size wound channels and therefor kill differently, that is more or less effectively.

    35W
     
  18. mcb

    mcb Member

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    Then what energy source causes the bullet to expand if not kinetic energy? Kinetic energy is the only energy a bullet has when it gets to the target to do anything. Just because the three different bullets behave differently does not mean kinetic energy is not the energy source doing the work it just means the geometry and material properties of the three different bullets behave differently to the energy dissipation during the impact.
     
    Last edited: Nov 27, 2019
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  19. Double Naught Spy

    Double Naught Spy Sus Venator

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    And isn't that just freaking amazing!! The math is the same, yet the results are different. What boggles my mind is that folks want to use math to predict behavior in living animals but fail to incorporate "living animal" in to the equation to make their predictions.

    That the projectiles behave differently is a HUGE consideration relevant to application. Math without application is just math.
     
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  20. mcb

    mcb Member

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    I agree you need to include the projectile and target properties in the math.
     
  21. Kleanbore

    Kleanbore Moderator Staff Member

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    What do you think causes a bullet to expand?
     
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  22. lysanderxiii

    lysanderxiii Member

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    The only projectiles whose expansion is not due to their kinetic energy are HE projectiles.

    These are extremely rare in the hunting applications.
     
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  23. fastbolt

    fastbolt Member

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    Math can fun, so I'm told. Like running, I never found it the most enjoyable pastime.

    My own personal opinion is that not only can none of the data points be used to accurately and consistently predict the "effectiveness" of the calibers/loads in the graphs when being used to produce GSW's, but neither can they be used to predict inherent accuracy of the listed loads.

    The unpredictable and potentially inconsistent human factors (shooter and person suffering the GSW) are going to distract from the beauty and "purity" of the math.

    :)
     
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  24. 35 Whelen

    35 Whelen Member

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    I KNEW I'd addressed this before, so rather than do the math all over again, lazy ol' me just searched for the post. I didn't realize how long ago it'd been; 5 1/2 years!!!

    Here's the post-

    Geez...this never ends...

    Energy does NOT kill! Case in point:

    A .30 caliber, 150 gr. bullet striking an animal @ 2700 fps possesses, generates, etc. 2427 ft. lbs. of energy.

    Another identically constructed .30 caliber, (hypothetically)15,000 gr. bullet striking an animal @ 270 fps likewise possesses, generates, etc. 2427 ft. lbs. of energy, same as the bullet in the above example.

    Get it? Identical amounts of energy from two .30 caliber bullets. Will they perform the same? Of course not. Our hypothetical 15,000 gr. bullet is travelling at a speed significantly less than an arrow fired from a compound bow. At that speed it won't even expand.


    Another example:

    A typical .44 Magnum load: 250 gr. SWC @ 1150 fps; Energy = 734 fp
    A typical .22 Hornet load: 46 gr. SP @ 2700 fps; energy - 744 fp

    Now, does anyone REALLY believe these two projectiles will kill exactly the same? Absurd.

    Energy does NOT initiate bullet expansion. Energy does NOT create hydrostatic shock. Math. Math. Math. That's all energy is. Period.

    Step AWAY from the keyboard and go hunting.


    Yet people STILL argue and talk about "energy dump", "the bullet passed through the animal and the energy was wasted", "the bullet stayed in the animal so the energy was all used", etc., etc., ad nauseam.

    So @Kleanbore @lysanderxiii can you see from my example of the .30 caliber bullets above that energy has nothing to do with bullet expansion?

    If you care to read the old thread you can find it here

    35W
     
    Last edited: Nov 28, 2019
  25. jmorris

    jmorris Member

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    And that ain’t that simple either because we could use an IV needle with very little energy and penetrate lots of materials completely but still not cause much damage or we could jump off a building and cause lots of damage to a very large area with zero penetration but lots of damage.

    Lot off variables, likely why this won’t be the last thread on the subject, this month ;)
     
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