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Thread: How Much Lead Shot per Cubic Inch?

 

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    NorthWoodsDiver's Avatar
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    How Much Lead Shot per Cubic Inch?

    I have tried to find a chart or some other figures via google with no luck so I thought I would try asking here instead.

    I am making a custom weight pack for sidemount diving and am trying to decide the proper size shot to use to get the weight I want in the size area I want to put it without buying some of each and playing around.

    So I am looking for the amount of lead shot per cubic inch for sizes #7, 71/2, 8, 81/2, and #9.

    #9 is .08 inches in diameter and # 7 is .100 inches so the bigger the number the smaller the diameter and its in .005" increments.

    I understand going with #9 will give me the most weight for my money but in this application the size of the package cant be changed, the size of the lead must be. #8 seems to be pretty common for scuba uses but I have seen numbers from#6 to #9 being used.

    I found info on the number of shot per ounce but that doesn't really help.

    The lead will be sealed in tubes made of 1" and 2" tubular webbing which slide into special fabric pockets I am making. all the pockets are the same length so if I want to vary the amount of weight I will need to use different size lead.

    Thanks a million. T
    If I don't find work soon I might have to take up Piracy...


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    reefduffer's Avatar
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    There's a fallacy implied in your question that I succumbed to as well in my initial reply. I shouldn't answer math problems before bed, the middle of the night seems to make for much more lucid thought.

    It seems "common sense" reasonable that smaller spheres will pack more densely. That turns out not to be the case. The packing volume of spheres is a constant regardless of the size of the spheres. See Sphere Packing -- from Wolfram MathWorld

    It depends on how tight the packing arrangement is (several are possible), but that's not really dependent on the size of the spheres. From the reference, the densest possible packing has the volume of the spheres being a little less than 78% of the volume of the space they occupy.

    There is one caveat in that argument, which is the boundary; the results in this theorem assume the volume filled is "large" compared to the size of the spheres. My intuition is that for 1" or 2" tubular webbing and lead shot of the size you're discussing, the boundary effect can be ignored. You can judge that for yourself, but it's still not meaningful to ask the question as "weight per cubic inch by shot size" without reference to the size of the container. If there's a significant boundary effect, it's a function of your container, so you'd have to "buy some of each and play around" to determine that.

    I was going to calculate the density for completeness, but that depends on the composition of your shot. Even "lead shot" may be an alloy, try googling that.
    "The Basis for Compositional Bullet Lead Comparisons," Forensic Science Communications, July 2002 is an interesting perspective for starters.

    But the big take-away is that I'd stop worrying about the size of the shot, I think they're all the same density for your purposes.

    All that said - from your description, "The lead will be sealed in tubes made of 1" and 2" tubular webbing" :
    Why would you care if the sealed webbing tubes are a little less than stuffed full?
    Does retention in the "special fabric pocket" rely on just friction?
    Last edited by reefduffer; January 30th, 2009 at 08:13 AM. Reason: Doh! moment wrt sphere packing.
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    dumpsterDiver's Avatar
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    The easy way to seal lead in tubes is to cut a section of bike inner tube (mountain bike for big and raod bike for smaller), tie the end off with a zip tie, pour lead in and then zip tie the other end. Then a quick wrap over the entire thing with duct tape to seal it up completely and to protect the inner tube. I made ankle weights like this and they lasted through years of commercail diving, although sometimes I had to remove some old tape and re-apply.
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    Quote Originally Posted by reefduffer View Post
    All that said - from your description, "The lead will be sealed in tubes made of 1" and 2" tubular webbing" :
    Why would you care if the sealed webbing tubes are a little less than stuffed full?
    Does retention in the "special fabric pocket" rely on just friction?
    I have a very limited space to work with and was trying to find the optimum size to use in the given space. Thanks for the help though. T
    If I don't find work soon I might have to take up Piracy...


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    siikik's Avatar
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    I realize there is airspace, but don't you get a cubic inch of lead shot per cubic inch? Just thinking about the actual question....



    Ken
    Experience is what you get when you didn't get what you wanted.

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    reefduffer's Avatar
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    Quote Originally Posted by siikik View Post
    I realize there is airspace, but don't you get a cubic inch of lead shot per cubic inch? Just thinking about the actual question....
    Ken
    Yes, you certainly get a cubic inch of lead shot, but only about 0.74 cubic inch of lead, which is what you need to know if you're concerned with how much it weighs.

    The original question essentially asked what that factor was as a function of shot size; the answer is that it's constant except when the container is not significantly larger than the shot diameter.

    Edit: My earlier statement that the factor is ~0.78 was due to my sloppy middle-of-the-night reading of the reference. The correct value is about 0.74.
    However it's still a constant, so the shot size still doesn't matter.
    I don't expect the discrepancy caused anybody real problems, but my apologies for any confusion.
    Last edited by reefduffer; February 4th, 2009 at 08:41 PM. Reason: Corrected numeric value of packing ratio.
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    I know I'm late to the game, and maybe nobody cares any more, but the 0.74 number assumes all the shot is the same size. If you mix the right sizes in the right amounts you can achieve substantially higher density.

    D

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