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Thread: Penetration of a Sphere formula?

  1. #1

    Penetration of a Sphere formula?

    Awhile back - I think in the Duplex .38 thread - there was mention of a formula that could roughly predict how a projectile would penetrate in ballistics gel. Sort of as a napkin hypothesis to test an idea prior to committing to gel testing.

    Does anyone here recall that formula?

    I'm trying to figure out what the minimum impact velocity would be for Steel Buckshot to hit 12" penetration.

    0.312" Steel Bearing = 32.4gr

    Turns out, Steel Bearings are super duper cheap - far below the cost of regular Buckshot. 10k 8mm Bearings is only $116, or $0.10 per 9 pellet load.

    The idea I had was for a 'Ultra Low Recoil' Buckshot load, that offers as close to 00 terminal performance with less recoil.

    Regular Lead 00 buck = 484gr @ 1325fps = Power Factor 641

    Reduced Recoil @ 1145FPS= PF 554

    vs


    9x Steel '0' Buck = 292gr

    x1400fps = 1267 ft/lbs / PF 407

    x1300fps = 1092ft/lbs / PF 378

    The question is how fast would the lighter steel buckshot need to be traveling at impact to hit 12" penetration?

  2. #2
    Site Supporter OlongJohnson's Avatar
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    One issue I can see with steel is it's far more elastic than lead, so it has much greater potential to bounce and ricochet at high speed off surfaces. Lead can do so, but the deformation that occurs when it impacts a surface consumes a great deal of energy. It might be an issue for accountability.
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    Quote Originally Posted by spyderco monkey View Post
    The question is how fast would the lighter steel buckshot need to be traveling at impact to hit 12" penetration?
    That thread mentioned Duncan MacPherson's equation. I think it's still under copyright so not sure about posting it.

    We also made reference to the mThor formula a lot. Again, due to copyright issues, I don't want to post it, but using using that formula, I calculated a .312'', 32.4 grain, round ball would penetrate 12'' at 1212 fps. This assumes no deformation, etc. Hopefully @the Schwartz will chime in if my number is off.

    I no longer have my copy of "Bullet Penetration" so can't run the numbers for you using MacPherson's equation.

  4. #4
    Quote Originally Posted by DMWINCLE View Post
    That thread mentioned Duncan MacPherson's equation. I think it's still under copyright so not sure about posting it.

    We also made reference to the mThor formula a lot. Again, due to copyright issues, I don't want to post it, but using using that formula, I calculated a .312'', 32.4 grain, round ball would penetrate 12'' at 1212 fps. This assumes no deformation, etc. Hopefully @the Schwartz will chime in if my number is off.

    I no longer have my copy of "Bullet Penetration" so can't run the numbers for you using MacPherson's equation.
    Excellent, thank you!

    I had figured it would be around 1200fps, based on the minimum velocity Brassfetcher found for non-deformed #4 buck to make it 12." So 1400fps should likely provide a comfortable margin for within 10 yards.

    Now I have to find the drag profile / BC of a sphere.

  5. #5
    Quote Originally Posted by OlongJohnson View Post
    One issue I can see with steel is it's far more elastic than lead, so it has much greater potential to bounce and ricochet at high speed off surfaces. Lead can do so, but the deformation that occurs when it impacts a surface consumes a great deal of energy. It might be an issue for accountability.
    I figure its a mixed bag in terms of risk.

    Cons:
    -potentially lethal if fired at a steel target at close range (might bounce straight back at the shooter)
    -serious skip/bounce off concrete

    Pros:
    -A stray pellet or outright miss will have a lethal range much shorter then Lead 00 due to the lower mass and inferior BC
    -Bearings should in theory group more tightly due to being non-deformed and perfectly round


    Ideally, what I had wanted was ZAMAC 3 00 buckshot. That would have comparable weight to 8mm steel, while being a bit softer (comparable to Brass) and more likely to deform rather then bounce. If Federal released a 'Ladies Home Defender' 12 gauge ultra lite load, I imagine thats what they'd use.

    But for home defense, I don't see much risk of ricochet, barring perhaps firing it into a granite counter top.

  6. #6
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    Quote Originally Posted by spyderco monkey View Post
    I figure its a mixed bag in terms of risk.

    Cons:
    -potentially lethal if fired at a steel target at close range (might bounce straight back at the shooter)
    -serious skip/bounce off concrete

    Pros:
    -A stray pellet or outright miss will have a lethal range much shorter then Lead 00 due to the lower mass and inferior BC
    -Bearings should in theory group more tightly due to being non-deformed and perfectly round


    Ideally, what I had wanted was ZAMAC 3 00 buckshot. That would have comparable weight to 8mm steel, while being a bit softer (comparable to Brass) and more likely to deform rather then bounce. If Federal released a 'Ladies Home Defender' 12 gauge ultra lite load, I imagine thats what they'd use.

    But for home defense, I don't see much risk of ricochet, barring perhaps firing it into a granite counter top.
    Ball bearings are going to be hard, very very hard and bouncy they’ll usually shatter before they deform much. Here’s something to thing about: the Russians started to produce lead cored ammo for all of their rifles (5.45x39, 7.62x39 and 9x39) when their steel cored ammo was causing too much collateral damage due to ricochets in urban environments.

    Just think about that for a minute Russians were bothered enough by the amount of unintended casualties caused by steel cored ammo with ricochets and overpenetration that they set up production lines for lead ammo. (These are the folks who pumped a movie theater full of fentanyl to end a hostage crisis and they ended up killing like half the hostages)

    I’m putting my hat in the this is a really bad idea camp.

    ETA here’s a video of a ball bearing being crushed by a hydraulic press, notice the minimal deformation before it explodes. Action starts at 1:09

    Last edited by Caballoflaco; 10-19-2020 at 09:14 PM.
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  7. #7
    Quote Originally Posted by DMWINCLE View Post
    That thread mentioned Duncan MacPherson's equation. I think it's still under copyright so not sure about posting it.

    We also made reference to the mThor formula a lot. Again, due to copyright issues, I don't want to post it, but using using that formula, I calculated a .312'', 32.4 grain, round ball would penetrate 12'' at 1212 fps. This assumes no deformation, etc. Hopefully @the Schwartz will chime in if my number is off.

    I no longer have my copy of "Bullet Penetration" so can't run the numbers for you using MacPherson's equation.
    Nope, DMWINCLE, your mTHOR calculations are ''right on the nose'' and your thoughtfulness and discretion in not publicly releasing MacPherson's and my equations is greatly appreciated.

    Since you mentioned MacPherson's WTI model—for a 0.312'', 32.4-grain steel sphere at 1,212 fps, MacPherson's model predicts a maximum penetration depth of 14.37'' and the Q-model (located on page 19 of QAS) predicts a maximum penetration depth of 14.02''.
    ''Politics is for the present, but an equation is for eternity.'' ―Albert Einstein

    Full disclosure per the Pistol-Forum CoC: I am the author of Quantitative Ammunition Selection.

  8. #8
    Quote Originally Posted by the Schwartz View Post
    Nope, DMWINCLE, your mTHOR calculations are ''right on the nose'' and your thoughtfulness and discretion in not publicly releasing MacPherson's and my equations is greatly appreciated.

    Since you mentioned MacPherson's WTI model—for a 0.312'', 32.4-grain steel sphere at 1,212 fps, MacPherson's model predicts a maximum penetration depth of 14.37'' and the Q-model (located on page 19 of QAS) predicts a maximum penetration depth of 14.02''.
    Wonderful, thank you!

    While I have you here, how would the performance be for a 0.33" Zinc Alloy 00 that weighs 33.9gr at the same impact velocity?

    The ball bearings are a simple and cheap option, but I think the ideal (if penetration is up to snuff) would be a Zinc Diecast 00 buckshot, as that would theoretically be less of a ricochet hazard.

  9. #9
    Quote Originally Posted by Caballoflaco View Post
    Ball bearings are going to be hard, very very hard and bouncy they’ll usually shatter before they deform much. Here’s something to thing about: the Russians started to produce lead cored ammo for all of their rifles (5.45x39, 7.62x39 and 9x39) when their steel cored ammo was causing too much collateral damage due to ricochets in urban environments.

    Just think about that for a minute Russians were bothered enough by the amount of unintended casualties caused by steel cored ammo with ricochets and overpenetration that they set up production lines for lead ammo. (These are the folks who pumped a movie theater full of fentanyl to end a hostage crisis and they ended up killing like half the hostages)
    Ummm, I'm not too sure about that lead ammo anecdote. For 5.45 for example, the Russians have been increasing the steel content and hardness; 7n6 -->7N10 -->7N22, the latter two featuring full length hardened steel penetrators.

    Meanwhile the US Army fields the M855A1 and M80A1 as standard issue ball, both featuring a large, exposed tip hardened steel penetrator.

    That said, firing against a hard surface like a AR500 target or brick wall with Ball Bearings would be a major hazard.

    I just don't think that hard surface hazard is present in most homes - where this sort of ultra low recoil round would be employed. Wood, plaster, drywall, etc would not present a ricochet hazard.

    Still, I can see why commercial loaded steel buckshot has not caught on; only takes one guy blasting a steel target with one to get a major lawsuit going. But for the handloader I think it has promise.

  10. #10
    Site Supporter Hambo's Avatar
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    Quote Originally Posted by spyderco monkey View Post
    Still, I can see why commercial loaded steel buckshot has not caught on.
    Read up on steel shot loads, and you'll find out why tungsten/bismuth are more popular.

    Loading it yourself, you're going to need steel wads and some basic data. There are reloaders who substitute 00 for birdshot, weight for weight, with powder and wad data, but I'm not one of them. I don't think I've read about anyone doing it with steel.
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