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Thread: How To Calculate Velocity For Different Barrel Lengths

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    How To Calculate Velocity For Different Barrel Lengths

    How To Calculate Velocity For Different Barrel Lengths

    I found these equations online; they were developed by Homer Powley. They seem to work well for rifles, and handguns, with the exception of revolvers.
    Also, they may not be accurate when calculating the velocity of barrel lengths where most of the powder is wasted, for example, a .45-70 from a 4-inch barrel will most likely produce an inaccurate value.
    However, a .223 from a 3-inch barrel was accurate to within 3 ft/s (it estimated 1,150 ft/s).

    Alright, here's how to do it.
    You need to know these values for your load.
    Also, remember you can calculate velocities for longer, as well as shorter, barrels.

    Vo = the original muzzle velocity (ft/s)
    B = the bullet weight (gr)
    C = the charge weight (gr)
    Lc = the cartridge overall length (in)
    Lb = the bullet length (in)
    Lbbl = the barrel length (in)
    D = the bore diameter (in)


    I'll do an example.

    .30-'06 Springfield 150-gr SP at 2,900 ft/s from a 24-in barrel.
    We'll see how it does from a 16.5-in barrel.

    Vo = 2,900 ft/s
    B = 150 gr
    C = 54.0 gr
    Lc = 3.34 in
    Lb = 1.10 in
    Lbbl = 24.0 in
    D = 0.308 in

    First we find the expansion ratio, Ro.

    Ro = 1/(1-([(B+C/3)(Vo/8000)^2]/C))
    Ro = 1/(1-([(150 gr+54.0 gr/3)(2,900 ft/s/8000)^2]/C))
    Ro = 1/(1-([(168)(0.131)]/C))
    Ro = 8.19
    The expansion ratio is 8.19.

    Now we want to find the expansion ratio for the new barrel.
    First find the Bullet Travel for the original barrel, To.

    To = Lbbl+Lb-Lc
    To = 24.0+1.10-3.34
    To = 21.8

    Now find the bore volume, Sbo.

    Sbo = To*0.773*D^2
    Sbo = 21.8*0.773*0.308^2
    Sbo = 1.60

    Now we need to find the "chamber volume", Sc.

    Sc = Sbo/(Ro-1)
    Sc = 1.60/(8.19-1)
    Sc = 0.222

    Now we can use Sc to calculate the expansion ration for the new barrel.

    Find the bullet travel and bore volume of the new barrel.

    T = Lbbl+Lb-Lc
    T = 16.5+1.10-3.34
    T = 14.3

    Sb = T*0.773*D^2
    Sb = 14.3*0.773*0.308^2
    Sb = 1.05

    Use the bore volume to find the new expansion ratio.

    R = (Sb/Sc)+1
    R = (1.05/0.222)+1
    R = 5.70

    Now use this equation and solve for velocity.

    V = 8000*sqrt((C*(1-(1/sqrt(sqrt(R)))))/(B+(C/3)))
    V = 8000*sqrt((54.0*(1-(1/sqrt(sqrt(5.70)))))/(150+(54.0/3)))
    V = 8000*sqrt((54.0*(1-(1/sqrt(2.39))))/168)
    V = 8000*sqrt((54.0*(1-(1/1.55)))/168)
    V = 8000*sqrt((54.0*(1-0.65))/168)
    V = 8000*sqrt((54.0*0.35)/168)
    V = 8000*sqrt((54.0*0.35)/168)
    V = 8000*sqrt(19.1/168)
    V = 8000*sqrt(0.113)
    V = 8000*0.337
    V = 2694 which rounds to 2690 ft/s.

    The velocity of the load from a 16.5-in barrel is estimated to be 2,690 ft/s.

    If you are likely to use this, I suggest saving the equations before they disappear.
    That's something I had a problem with.

    Any questions, send me a PM.

    After all those formulas you may be in need of a little levity. Enjoy!

    The Trololo Man's Website

  2. #2
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    Can't I just use a chrono, please? I hate math!

  3. #3
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    Can't I just use a chrono, please? I hate math!
    But how do you chrono a gun you don't have?

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    ballisticsbytheinch.com
    Teachers can learn ua the rules;
    Experience teaches you the exceptions

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    Cool! I have frequently wondered about velocity for several of my toys.

    Thank you now. I will probably not have nice things to say about you later, but thank you now...

  6. #6
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    Any idea about the assumptions made by Powley while developing the formula?

    Sometimes Powley's work is accompanied by a list of assumptions (for instance, assumes a fast powder rather than a slow powder; or assumes jacketed bullet vs. lead bullet; or assumes cold bore temperature; etc.).

  7. #7
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    Naah, I'll just use the chronograph. As long as I don't shoot the darned thing, it works good. Actual measurement as opposed to estimates.

    I wonder how Powley accounted for the individual differences in barrels? I know that the same load shot through two different barrels might give differences in velocity. And I've got some loads that are significantly different from published velocities when fired from my rifles.

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    But how do you chrono a gun you don't have?
    I guess I missed something--why am I estimating the balistics of a short-barrel gun I don't have, again?

    ("Would the gentleman please get into the spirit of the proceedings...")

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    I wonder how Powley accounted for the individual differences in barrels? I know that the same load shot through two different barrels might give differences in velocity. And I've got some loads that are significantly different from published velocities when fired from my rifles.
    Dennis, it appears to me that his calculations just adjust for length in two barrels that are "equal" except for length. Of course no two barrels are exactly equal...
    Paul
    People have some respect for the complexity of technology. But almost every ignorant fool thinks he understands money and economics.

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    I see where this would be helpful. The manuals always specify loads for a particular length barrel, but invariably my barrel is a different length. It'd be even better if it factored in for different twist rates.
    “As long as we allow an individual right to trump public safety, families are going to lose their loved ones…"
    - Kristin Comer, Executive Director, Washington CeaseFire

  11. #11
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    For example, a while back I couldn't find chrono data for a .40 out of a 3-in barrel.

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    Neat formula, fun exercise in ballistics and all and might even got one pretty close of an estimate. But, till you run it through a chrono outof your gun you won't know for sure.
    Some people are like slinkies. Not really good for anything but they still bring a smile to your face when you push them down a flight of stairs.

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    This is just too much. For a lot of these questions, might I suggest:
    http://www.ballisticsbytheinch.com/
    These guys set out to prove exactly what the math tries to do here, and they most certainly DO NOT agree!
    If I don't own a caliber/rifle, I don't care what it does. If I want to know, I can get a really good general idea. More exceedingly excellent stuff here:
    http://forums.handloads.com/

  14. #14
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    boberama,

    In the final equation to solve for V you have an odd operation (it seems) dealing with R—the square root of the square root of R.

    Is that a typo, or should it be the fourth root of R?

    Perhaps the easiest way to show it?

    Edit: an easier way to show it and not have to use graphics:

    V=(8000*(((C*(1-(1/((R^.5)^.5)) / (B+(C/3)))^.5))))
    or
    V=(8000*(((C*(1-(1/(R^.25) / (B+(C/3)))^.5))))

    Re-Edit: OOPS! Was looking at a copy of the graphics only and when I scrolled up, later, saw you did that.
    Last edited by ClayInTx; October 15th, 2010 at 12:53 PM. Reason: Show equation on one line.

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    Yup, you could do the 4th root instead of the sqrt(sqrt( that I have.

    I find it's easier to punch in on my calculator though.

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    I am a mathematician. I am also a reloader with 40 years experience.

    I never let my mathematician identity put pressure on my reloader identity.

    Ergo, I do not have to deal with weird equations and functions when reloading and therefore I can concentrate on the real world of bullet seating, OAL, cartridge prep, etc etc.

    If you think you need a function to determine an important factor in reloading, then you have not mastered the reloading literature. Believe me, in a book somewhere is the answer to any reloading question.

  17. #17
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    I use the book for reloading,
    However,
    The equations serve as an estimate before trying something different; or sometimes just for grins to see what might be.

  18. #18
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    I use the book for reloading,
    However,
    The equations serve as an estimate before trying something different; or sometimes just for grins to see what might be.
    ^Yup, that sums it up. Obviously, don't use these equations to work up new loads!

  19. #19
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    I am a mathematician. I am also a reloader with 40 years experience.

    I never let my mathematician identity put pressure on my reloader identity.

    Ergo, I do not have to deal with weird equations and functions when reloading and therefore I can concentrate on the real world of bullet seating, OAL, cartridge prep, etc etc.

    If you think you need a function to determine an important factor in reloading, then you have not mastered the reloading literature. Believe me, in a book somewhere is the answer to any reloading question.
    You mean I should depend on someone else to do what I can do myself, and just HOPE that their work is correct and assume that mine would not be? That sounds like reading mainstream media to determine what my stance on 2nd amendment issues should be... (not stated confrontationally, just sayin'... ) It might not be for you, but I like doin' stuff for myself... Then I know it's right.
    Last edited by Coolbreeze8804; October 16th, 2010 at 08:34 PM. Reason: spelling... which was wrong the first time. How ironic! ha ha ha.....

  20. #20
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    The equations can be used for other than reloading.

    My Lyman’s gives velocity figures for only one length barrel. The equations can estimate what would be the velocity for another length. My barrels are not all the same as listed in Lyman’s.

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    As the founder of Faber College said, knowledge is good.
    Paul
    People have some respect for the complexity of technology. But almost every ignorant fool thinks he understands money and economics.

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    Thumbs up

    You ROCK, boberama! I have been looking around for this for a couple of years now.
    Texas, by God!

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