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Thread: A Little Math That Will HOPEFULLY Be Helpful

  1. #1
    Boolit Buddy
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    A Little Math That Will HOPEFULLY Be Helpful

    It pains me to see people struggle to get answers to simple questions. I have been going through the past year's threads in this subsite ("Swaging") and saw several common questions. One of them was some form of this: "How long do I need my core to be if I want it to weigh "X" grains?"

    The formulas for obtaining the core length are not difficult to deal with, and I suspect that most folks 'get there' PDQ. Nonetheless, I thought I'd offer the following "condensation" for those that would like the 'thing' condensed into the most succinct, and hopefully useful form.

    Skip to the PS if you don't care about "how he got there".

    Cores are cylinders. The formula for the volume of a cylinder is:

    V = pi * r2 * h

    Where:
    "V" = the Volume,
    pi = 3.14,
    r2 = the radius of the core multiplied times itself, and
    h= the height or length of the core - the value we are looking for.

    Since it's "h" we are looking for, we rearrange the equation to:

    h = V / (pi * r2). In words: the height of the cylinder (our core) equals the volume of the core divided by pi times the radius of the core times itself.

    Another value is needed - the density of lead - to complete this "condensation". (I'll call that "d".) The theoretical density of pure lead is 11.34 GRAMS per cubic CENTIMETER. Since most folks want their core dimensions in inches and weight in grains, the density of lead in GRAINS PER CUBIC INCH is 2,867.35

    One can get the mass (weight, here on earth) of some solid if one knows its density. The formula is:

    m = V * d

    Where:
    "m" = the weight we want the core to be,
    "d" = 2,867.35 grains per cubic inch.
    "V" = the volume of the core just like in the above equation, AND THAT IS IMPORTANT because it allows us to combine the equations into ONE,

    Since m = V * d,
    V = m/d.
    Therefore, we can substitute "m/d" into the FIRST equation (the volume of a cylinder) which becomes:

    h = (m/d)/(pi * r2)

    In words: The height of the core equals the weight of the core divided by the density lead divided by pi times the radius of the core times itself.

    While that might not look "simple", stick with me a minute more and I think it will be.

    There are some constants and 'knowns' that are going to simplify matters.

    We 'know' what we want our core to weigh, so we 'know' "m".
    We 'know' what the value of pi is.
    We 'know' what the diameter of our core is, therefore we know what its radius is.
    We 'know' the density of lead.
    So...

    Here's an example:
    I swage 8mm bullets. The cores I use are 0.250" in diameter, making their radius 0.125" in diameter. That value times itself is 0.125 * 0.125 = 0.015625 inches. That's r2 FOREVER for a cylinder that is 0.250" in diameter. Therefore, calculated ONCE forever for my cores, that value NEVER changes.

    My jackets weigh ~43 grains. I want a final weight of ~125 grains. Therefore, I want the core to weigh 125 grains minus 43 grains = 82 grains. That's my "m" for core for a 125-grain bullet.
    The density of lead in grains per cubic inch is 2,867.346.

    Substituting into the equation what we know, we get:

    h = (82/2867.346)/(3.14*0.015625),

    Therefore, our core length should be 0.58 inches. If I want to change the weight of the bullet, the ONLY number I have to change in the equation is "m", in this case the 82. The other numbers are CONSTANT - FOREVER for my bullets with 0.250" cores.

    "Doing the algebra", the density of lead, pi, and the radius of the core times itself can all be combined into ONE NUMBER: 2867.346 * 3.14 * 0.015625 = 140.75.

    THEREFORE, for MY 8mm bullet cores, all I have to do to find the length of a core for a specific weight finished bullet is divide the core weight I want by 140.75.

    For example, let's say I want a finished bullet weight of 150 grains. The core would need weigh 150 - 43 = 107 grains. 107 divided by 140.75 = 0.76. Therefore, the core length necessary for a 150-grain bullet would be 0.76 inches long.

    Let me take one more moment and show the difference for a different core diameter (caliber). Let's say the core material for a .224 bullet is 0.125" in diameter. (1/8th inch lead wire.) The radius is 0.0625 inches. That value times itself is 0.00390 square inches. Let's say the jackets weight 20 grains and I want the finished bullet to weight 55 grains. The core then needs to weigh 35 grains. Once again, 2867.346 * 3.14 * 0.00390 equals our "CONSTANT" for the .224 bullet with a 0.125 core. That number is 36.41. Therefore, dividing 35 grains (the weight we want our core to be) by 36.41, we get a core length of 0.96 inches.

    Before anyone howls too loudly, I don't swage .22 caliber bullets, so the above weight of the jacket, (20 grains) and the core diameter (0.125") are just WAGS on my part to illustrate how simple it is to go from one core diameter to another.

    I HOPE this has been helpful/useful. That was the intent.

    Paul

    PS
    In an attempt to reduce the number of operations to the minimum, you don't even have to find the radius. To get THE Number, just square the diameter and multiply by 2252.009.

    So the steps reduce to three:
    1) Square the diameter of core material, (the more precise the measure of the diameter of the core material, the better the estimate of length will be),
    2) Multiply by 2252.01, SAVE RESULT
    3) Divide desired core weight by the result of #2. The answer to that division is the length of the core for the weight you want it to be.

    Therefore, all you really need to determine the length of a LEAD core of a given bullet weight is the diameter of the core and the weight you want it to be. (If you don't have a "square" key on your four-function calculator, you can divide the DIAMETER by 16. The result is the same as squaring the RADIUS.)

    Paul
    Last edited by gitano; 05-02-2015 at 03:54 PM.

  2. #2
    Frosted Boolits

    IllinoisCoyoteHunter's Avatar
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    Thanks for the info! There is a fellow on here who has put all of these calculations in an excel program. I forget who did it but they emailed it to me and it makes figuring cores really simple and fast. Great post!
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  3. #3
    Boolit Buddy
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    I use a calculator like this one, choose cylinder, lead as the material, and set quantity to 7000. By setting the quantity to 7000 it will convert the results from lbs to grains http://www.custompartnet.com/quick-t...ght-calculator

    I do the the actual calculations sometimes but find the online calculators to be more efficient for my needs
    Last edited by goblism; 05-02-2015 at 09:40 AM.

  4. #4
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    that's the same formula you use to figure the volume of pipe [any cylinder really]
    pi x Radius squared, times length.

  5. #5
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    Impressive, thanks. My head still hurts though...

  6. #6
    Boolit Mold
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    Why all the math? I use an electronic scale, place the jacket on it and cut or cast my lead slugs to a weight exceding the finished weight by several grains and then swage (bleed off) the core to the weight plus the jacket equals the finished weight. Simple enough for me.

  7. #7
    Boolit Buddy
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    IllinoisCoyoteHunter - I use an excel spreadsheet and just create a table of values for each 5 grains of weight within the range of weights I am interested. However, LOTS of people don't have access to excel or aren't particularly facile with it. I thought about presenting the spreadsheet but what I really wanted to do was present something that was as simple as possible. The above four steps (only three math operations - two multiplications and one division), can be accomplished on a 4-function calculator.

    goblism - I saw that calculator when I was looking through the 'archives'. It is convenient for sure, but what I offered above is even more convenient I think as one doesn't even need to turn on the computer to get the information one wants/needs.

    Correct, runfiverun.

    MrWolf - I was going to skip the explanation, but I just couldn't bring myself to do that. I thought if I did, more than one would either challenge the 'condensation' or ask for explanation. I made it as 'non-mathy' as I could.

    forwardgunner - Far be it from me to suggest that anyone "fix what ain't broke". If the process you describe 'works' for you, have at it. Personally, I don't care for 'trial and error' when a non-trial-and-error method exists. Trial-and-error methods always lead to some waste. Waste, be it time, effort, or resources, "bugs" me. I did my core length determinations exactly the way you do them for a while, but got tired of "starting over" every time I changed bullet weights, and i wanted to minimize (not eliminate) 'squeeze-out' when I swaged my cores. Like I said, I'm not trying to talk anyone in to changing, just offering an alternative to trial and error to those that might be looking for one.

    Paul

    PS - For anyone wanting a copy of my excel spreadsheet, just shoot me a PM. Still, I think one square, one multiply, and one divide, without having to "go to" my computer or open and use excel, is just too easy. In fact, after the initial calculation to determine "THE" number (140.75 for my 0.250" cores), there is only ONE calculation necessary: Divide the desired core weight by that number. I don't know how to get it simpler than that since I keep a calculator right beside my press. On a personal note, I'll be 'moth-balling' my excel spreadsheet for core calculations.

    Paul
    Last edited by gitano; 05-02-2015 at 04:01 PM.

  8. #8
    Boolit Buddy
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    I decided that if I wanted to truly HELP, I would just "do the math" and provide the results in a table here. I found a guy on Ebay that is selling lead wire for bullet swaging. The smallest diameter he sells is 0.180" and the largest is 0.475". I'll run a table from 0.180 to 0.500. I can't get all of them "snipped" into one table so there are 10 separate ones. Here ya go:




















    So, all 'you' have to do is take the number from the column labeled "THE Number" that corresponds to the diameter of your core and divide the weight that you want your core to be by that number. The result will be the length in inches of your core. Personally, since I swage my cores, I would add maybe "a little" (say, 0.05"), to that resulting LENGTH figure (NOT to THE Number), for "sqeeze out". (Note that at a wire diameter of 0.250", THE Number is 140.75 - the same as obtained in the OP.)

    Paul

    PS - For those that might be interested, I would appreciate it if you would please check this against what you have determined for your actual core length values for a given weight, and report in this thread if the numbers jibe.

    PPS - I should note that a difference/error of 0.001" in the TRUE diameter of your core WIRE and what you put in the "equation" for finding THE Number will result in an error of 2.252 units in THE Number.

    Paul
    Last edited by gitano; 05-02-2015 at 04:04 PM.

  9. #9
    Boolit Buddy
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    I don't like the name "THE Number". Let's call it the "core length constant" or CLC. At least in this thread. Actually that could "work". As it has been described in this thread, it is unique for pure lead. Were one to use a different metal or alloy, a subscript could be added. For example: Using clip on wheel weights, the abbreviation could be CLCcoww. For lead, CLCpb.


    Paul

  10. #10
    Boolit Buddy
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    So this evening I was in my 'gun room' mostly looking for something to do when I decided to swage some 8mm bullets. I decided I would make 136-grainers. (Weight selection is a long story about which I will spare you.) Soon as I decided on a weight, I subtracted the jacket weight from 136 and got 94.4. Shiite muslims! I'll have to go get on my computer to calculate the length of the .250" wire I use for cores. Wait a minit! I remembered the 140.75 CLCpb for .250" wire. I grabbed the calculator that was right beside the press and divided 94.4 by 140.75... 0.67 inches. I decided to add 0.03" and make it a 'round' 0.7". I cut a piece of wire 0.7" long and weighed it. 100.8 grains. Excellent! I measured 7.125" of wire and cut that off of the spool and commenced to swage 10 more cores right at 94.4 grains. (In "production mode" I was getting pre-swage weights of 99.4 grains.) I was 'squirting' about 5 grains per core. That 'works' for me.

    Paul

  11. #11
    Boolit Buddy
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    there is one small problem with your formula
    pi R round
    cake R square

  12. #12
    Boolit Buddy



    xman777's Avatar
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    Quote Originally Posted by varmint243 View Post
    there is one small problem with your formula
    pi R round
    cake R square
    I'll be needing a cylinder of milk in either case.

  13. #13
    Boolit Buddy
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    I don't know if you two know Justin Wilson - The Cajun Chef - but he was a great story/joke teller. He used to tell as story about a boy from the bayou that went off to college and when he came home after his first semester, his dad wanted him to say something "smart" to show what he learned. The boy thought for a minute and said, "Pi R Squared". His father hit him upside the head and said; "Hooeee, boy! Everbody knowd pie are round!" (It was much funnier when Wilson told it with his cajun accent.)

    Paul

  14. #14
    Boolit Master



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    Paul,
    I missed this the first time around. I lost spread sheet in a computer crash, thanks for the list. I could not get my spread sheet to do what you accomplished. Now all I need to do is add a core weight and I can set the squirt die and core cutter a lot closer, now I need a couple core molds and squirted dies since I'm converting cases to jackets. Could you pm me a live copy. All I can get is a picture of the spread sheet.
    Thanks,
    Bill

  15. #15
    Boolit Bub
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    Spreadsheet

    Hey all,

    I took the formula outlined by gitano and turned it into a spreadsheet.

    You can download the spreadsheet at:
    https://docs.google.com/spreadsheets...gid=1900654019

    Thanks to gitano for the lesson.

    CM

  16. #16
    Boolit Master
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    Thanks but sheet will not download and I use Excel but don't know where to enter data.
    NRA Life Member

  17. #17
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    Quote Originally Posted by gitano View Post
    It pains me to see people struggle to get answers to simple questions. I have been going through the past year's threads in this subsite ("Swaging") and saw several common questions. One of them was some form of this: "How long do I need my core to be if I want it to weigh "X" grains?"

    The formulas for obtaining the core length are not difficult to deal with, and I suspect that most folks 'get there' PDQ. Nonetheless, I thought I'd offer the following "condensation" for those that would like the 'thing' condensed into the most succinct, and hopefully useful form.

    Skip to the PS if you don't care about "how he got there".

    Cores are cylinders. The formula for the volume of a cylinder is:

    V = pi * r2 * h

    Where:
    "V" = the Volume,
    pi = 3.14,
    r2 = the radius of the core multiplied times itself, and
    h= the height or length of the core - the value we are looking for.

    Since it's "h" we are looking for, we rearrange the equation to:

    h = V / (pi * r2). In words: the height of the cylinder (our core) equals the volume of the core divided by pi times the radius of the core times itself.

    Another value is needed - the density of lead - to complete this "condensation". (I'll call that "d".) The theoretical density of pure lead is 11.34 GRAMS per cubic CENTIMETER. Since most folks want their core dimensions in inches and weight in grains, the density of lead in GRAINS PER CUBIC INCH is 2,867.35

    One can get the mass (weight, here on earth) of some solid if one knows its density. The formula is:

    m = V * d

    Where:
    "m" = the weight we want the core to be,
    "d" = 2,867.35 grains per cubic inch.
    "V" = the volume of the core just like in the above equation, AND THAT IS IMPORTANT because it allows us to combine the equations into ONE,

    Since m = V * d,
    V = m/d.
    Therefore, we can substitute "m/d" into the FIRST equation (the volume of a cylinder) which becomes:

    h = (m/d)/(pi * r2)

    In words: The height of the core equals the weight of the core divided by the density lead divided by pi times the radius of the core times itself.

    While that might not look "simple", stick with me a minute more and I think it will be.

    There are some constants and 'knowns' that are going to simplify matters.

    We 'know' what we want our core to weigh, so we 'know' "m".
    We 'know' what the value of pi is.
    We 'know' what the diameter of our core is, therefore we know what its radius is.
    We 'know' the density of lead.
    So...

    Here's an example:
    I swage 8mm bullets. The cores I use are 0.250" in diameter, making their radius 0.125" in diameter. That value times itself is 0.125 * 0.125 = 0.015625 inches. That's r2 FOREVER for a cylinder that is 0.250" in diameter. Therefore, calculated ONCE forever for my cores, that value NEVER changes.

    My jackets weigh ~43 grains. I want a final weight of ~125 grains. Therefore, I want the core to weigh 125 grains minus 43 grains = 82 grains. That's my "m" for core for a 125-grain bullet.
    The density of lead in grains per cubic inch is 2,867.346.

    Substituting into the equation what we know, we get:

    h = (82/2867.346)/(3.14*0.015625),

    Therefore, our core length should be 0.58 inches. If I want to change the weight of the bullet, the ONLY number I have to change in the equation is "m", in this case the 82. The other numbers are CONSTANT - FOREVER for my bullets with 0.250" cores.

    "Doing the algebra", the density of lead, pi, and the radius of the core times itself can all be combined into ONE NUMBER: 2867.346 * 3.14 * 0.015625 = 140.75.

    THEREFORE, for MY 8mm bullet cores, all I have to do to find the length of a core for a specific weight finished bullet is divide the core weight I want by 140.75.

    For example, let's say I want a finished bullet weight of 150 grains. The core would need weigh 150 - 43 = 107 grains. 107 divided by 140.75 = 0.76. Therefore, the core length necessary for a 150-grain bullet would be 0.76 inches long.

    Let me take one more moment and show the difference for a different core diameter (caliber). Let's say the core material for a .224 bullet is 0.125" in diameter. (1/8th inch lead wire.) The radius is 0.0625 inches. That value times itself is 0.00390 square inches. Let's say the jackets weight 20 grains and I want the finished bullet to weight 55 grains. The core then needs to weigh 35 grains. Once again, 2867.346 * 3.14 * 0.00390 equals our "CONSTANT" for the .224 bullet with a 0.125 core. That number is 36.41. Therefore, dividing 35 grains (the weight we want our core to be) by 36.41, we get a core length of 0.96 inches.

    Before anyone howls too loudly, I don't swage .22 caliber bullets, so the above weight of the jacket, (20 grains) and the core diameter (0.125") are just WAGS on my part to illustrate how simple it is to go from one core diameter to another.

    I HOPE this has been helpful/useful. That was the intent.

    Paul

    PS
    In an attempt to reduce the number of operations to the minimum, you don't even have to find the radius. To get THE Number, just square the diameter and multiply by 2252.009.

    So the steps reduce to three:
    1) Square the diameter of core material, (the more precise the measure of the diameter of the core material, the better the estimate of length will be),
    2) Multiply by 2252.01, SAVE RESULT
    3) Divide desired core weight by the result of #2. The answer to that division is the length of the core for the weight you want it to be.

    Therefore, all you really need to determine the length of a LEAD core of a given bullet weight is the diameter of the core and the weight you want it to be. (If you don't have a "square" key on your four-function calculator, you can divide the DIAMETER by 16. The result is the same as squaring the RADIUS.)

    Paul

    I'm dizzy.

  18. #18
    Boolit Buddy
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    For what it's worth, I didn't have any problem downloading chaoticmachinery's spreadsheet.

    Paul

  19. #19
    Boolit Master
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    Thanks for taking the time to walk us thru the calculation of core length at “x” diameter of core. I sat down a couple of weeks ago and started going thru the gymnastics involved and then going from specific gravity of lead to grains of lead and I think it took about 30 - 40 minutes of trying to remember stuff I had not used in a while! I did finally grind out an answer, but I wish I had checked here first!
    Decreed by our Creator: The man who has been made able to believe and understand that Jesus Christ has been sent into this world by the Father has been born of the Spirit of God. This man shall never experience spiritual death. He will live forever!

  20. #20
    Boolit Man SSG_Reloader's Avatar
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    Wow. That is unbelievably helpful and easy. Thank you!

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