New Formula for Gyroscopic Stability of Open Tipped Match Style Rifle Bullets

Discussion in 'Rifles, Bullets, Barrels & Ballistics' started by Michael Courtney, Jan 19, 2014.

  1. Michael Courtney

    Michael Courtney Silver Member

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    New Formula for Gyroscopic Stability of Open Tipped Match Style Rifle Bullets

    A paper describing our new formula for the gyroscopic stability of open tipped match bullets has just been published by Cornell University Library. Don Miller knew that the assumption of constant density used to develop his original twist formula would tend to underestimate the stability of open tipped match bullets, and shared some very good ideas which proved useful in formulating a more accurate equation. I have a spreadsheet implementation of the new formula, along with the previous formulas for constant density bullets and plastic tipped bullets. See: http://forum.accurateshooter.com/index.php?topic=3834705.new#new for download.

    http://arxiv.org/ftp/arxiv/papers/1401/1401.4187.pdf

    Abstract: Earlier work has produced formulas for predicting stability of rifle bullets of near uniform density and also for plastic-tipped rifle bullets. These formulas have been shown to be accurate to within 5%. However, the original Miller twist formula for metal bullets of near uniform density underestimates the stability of match style open tipped rifle bullets having a significant empty volume in the tip. This paper presents a new formula for accurately estimating the stability of these open tipped match style rifle bullets from parameters easily obtained such as the bullet mass, length, and depth of the empty space in the tip. The formula is tested by measuring the aerodynamic drag vs. predicted stability of several bullets over a range of stabilities.
     
  2. Michael Courtney

    Michael Courtney Silver Member

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    Since some people missed it I should emphasize the need to determine and enter the right length for the full density part of the bullet.

    For plastic tipped bullets, the full density length is the total length minus the length of the plastic tip (the length of the metal part of the bullet).

    For open tipped match bullets, the full density length is the total length minus the depth of the open tip (as determined by inserting a mechanical pencil lead or small drill bit).
     
  3. Len Backus

    Len Backus Administrator Staff Member

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    Michael, thanks!

    I will publish this next month as a feature article.
     
  4. Michael Courtney

    Michael Courtney Silver Member

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    Awesome!
     
  5. Michael Eichele

    Michael Eichele Well-Known Member

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    Excellent! It's good to see advancement in equations for more detailed results by accounting for more variables.

    Thank you.

    M
     
  6. Michael Courtney

    Michael Courtney Silver Member

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    There are important differences between Sg (gyroscopic stability) and dynamic stability. If a bullet has gyroscopic stability when it leaves the muzzle, it will maintain gyroscopic stability at all ranges, as Litz describes in his book on applied ballistics.

    Dynamic stability is different, as shown in the figure attached for the M855 bullet.

    Inferences regarding dynamic stability should not be made from Sg values. Some references on dynamic stability:

    http://www.dtic.mil/ndia/2011ballistics/11894.pdf

    http://www.arl.army.mil/arlreports/2010/ARL-TR-5182.pdf

    http://www.fulton-armory.com/faqs/Genl-FAQs/Fly/longr.htm
     

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