Terminal Ballistics

Discussion in 'Off Topic' started by pokute, Dec 5, 2014.

  1. pokute

    pokute Sincere as a $5 funeral

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    Historically, the discussion of how a bullet affects the target has been a contentious topic. The source of contention was and is, as with most things, ignorance.

    Lets take a look at terminal ballistics for two hypothetical rounds:


    1. 135gr bullet at 1500fps (357 magnum)
    2. 300gr bullet at 1000fps (44M or 45LC)
    I have chosen these examples because though they have almost exactly the same kinetic energy, they will have dramatically different terminal ballistic effects given a variety of targets. Assume the bullets are both jacketed semi-wadcutter solid point designs.

    First, I want to make a point that is usually not made clearly. Bullet #2 has the same kinetic energy as bullet #1, but it has 50% more momentum. Think of it as the difference between a little rock hammer and a pickaxe both being swung by the same arm.


    • Ballistic Pendulum
    A ballistic pendulum is a target that is designed to measure kinetic energy. An ideal ballistic pendulum would record a value exactly proportional to the kinetic energy of the projectile. In real life, it doesn't work, because the bullet and pendulum both deform, dissipating energy in complex ways. Ballistic pendulums are only accurate at relatively low velocities.

    • Metal plate hanging on a chain
    What the heck?! Where did I get this from?! Well, it's what we non-ballisticians usually have ready access to, and it happens to demonstrate differences due to momentum pretty convincingly. The 135gr high velocity bullet will dance a 5 lb plate noticeably. The 300gr bullet will swing the plate clear up over the bar that the chain is hanging from. Hmmm... interesting. Why is that? Well, the terminal behavior in this case is dominated by momentum transfer from the bullet to the plate - The 300gr has 50% more momentum, and the more massive bullet at a lower velocity transfers momentum more efficiently over time. The time dependent components are described as "kinematic" effects. A complex topic I will leave for independent study if you care to pursue it.

    • Small animal
    Considering something like a rabbit, the small high velocity bullet hitting it center of mass has at least the possibility of blowing it to bits due to cavitation (temporary wound channel expansion), an effect whereby water vaporizes momentarily under a high shear gradient - And the collapse of the "bubble" is so rapid that it creates a shock wave that damages even more tissue than the preceding shear wave. The rabbit may not explode most of the time, but it can happen if the temporary cavity is not contained by the body. The big slow bullet #2 goes right through, bruising, crushing, and smashing it's way along a nearly straight path, leaving a couple of big holes at each end.
    • Medium to large animal
    The small, high velocity bullet will generally produce a large temporary wound channel via cavitation, and then follow an unpredictable path, doing more or less damage. The large, slower bullet will tend to do the same thing it did to the small animal, tending to follow a straight path. The relative effects of the two offer no basis for comparison that I can see, though Julian Hatcher gives the nod to the round with the larger sectional area, momentum being equal.
    Do note that the examples were chosen to exclude well known differences between pistol rounds and rifle rounds at velocities sufficient to produce shock waves in water, which occurs at roughly 50% of the speed of sound in water, or about 2400 fps.

    For thorough practical discussion of the topic, I can think of no better reference than Julian Hatcher's Textbook of Pistols and Revolvers.
     
    Last edited: Dec 8, 2014
  2. gumpy

    gumpy Lifetime Supporting Member Lifetime Supporter

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    I'd love to have access to your library! Some more stuff I Had noticed without knowing the correct why.
     

  3. Winds

    Winds Supporting Member Supporter

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    Thank you for such an informative post.
     
  4. pokute

    pokute Sincere as a $5 funeral

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    I kind of waltzed around Julian Hatcher's work there, and felt I should elaborate.

    Hatcher devised a simple, reasonable method of comparing the potential effectiveness of different rounds. He multiplied the momentum by the nominal cross sectional are of the round. This quantifies the advantage of the larger caliber round over the smaller. It is useful for directly comparing bullets of similar overall design. I believe it is a good metric.

    Calculating the Hatcher Number:

    w = bullet weight in grains
    v = velocity in feet-per-second
    d = bullet diameter in inches

    H (Hatcher Number) = w * v * d * d * 0.0001122

    The mathematically adept will bridle at the funny constant - Please accept that I wanted anybody to be able to do the calculation on their calculator without confusion.

    Some typical values:

    22 LR HV
    40gr * 1235fps * 0.223 * 0.223 * 0.0001122 = 0.3

    38 Special - 158gr 900fps
    158gr * 770fps * 0.357 * 0.357 * 0.0001122 = 1.7

    9mm +P+
    115gr * 1400fps * 0.355 * 0.355 * 0.0001122 = 2.3

    357 Magnum
    158gr * 1485fps * 0.357 * 0.357 * 0.0001122 = 3.4

    10mm Norma
    200gr * 1200fps * 0.4 * 0.4 * 0.0001122 = 4.3

    45 ACP
    230gr * 900fps * 0.452 * 0.452 * 0.0001122 = 4.7

    44 Magnum
    240gr * 1500fps * 0.429 * 0.429 * 0.0001122 = 7.4

    45 Colt
    325gr * 1325fps * 0.454 * 0.454 * 0.0001122 = 10.0

    454 Casull
    400gr * 1400fps * 0.452 * 0.452 * 0.0001122 = 12.8
     
    Last edited: Jan 9, 2015
  5. pokute

    pokute Sincere as a $5 funeral

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    It never occurred to me to read the FBI ballistics report summaries. Not surprisingly, they agree 100% with Julian Hatcher's findings. Here's a link to the various summary reports, for anyone who cares to read them:
    http://www.firearmstactical.com/wound.htm
     
  6. gumpy

    gumpy Lifetime Supporting Member Lifetime Supporter

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    Interesting stuff! Thanks
     
  7. pokute

    pokute Sincere as a $5 funeral

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    Over the last few days I've been reading Wound Ballistics: Basics and Applications (Yes, you can download it from that page - For free). In chapter 3, terminal ballistics studies and calculations are compared in depth. The author's conclusion is that no good metric exists, and that even conclusions based on analysis of actual shooting incidents are... Inconclusive!

    He also points out that many historically proposed metrics tend to agree because they proceed from similar assumptions, not because the assumptions are correct.
     
    Last edited: Jun 5, 2015
  8. Geezer

    Geezer New Member

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    Terminal? I didn't even know it was sick.
     
  9. pokute

    pokute Sincere as a $5 funeral

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    What happened to the Dislike This Post button?!
     
  10. squirrelhunter

    squirrelhunter Well-Known Member

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    You mean we had one???:eek:
     
  11. pokute

    pokute Sincere as a $5 funeral

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    I'm sure I saw it once or twice... Somewhere... Uh...
     
  12. squirrelhunter

    squirrelhunter Well-Known Member

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    Alright,who lost the button?!?!?:eek:
     
  13. Straightwall

    Straightwall New Member

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    You never know what you've got 'til it's gone.