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Thread: Simple closed-form extensions of the Alekseevskii-Tate equation for rigid penetrators

  1. #11
    That's an interesting video, especially the portion that starts at 4:54 that shows the hydrodynamic flow phase of the JHPs deforming in the first few inches of gelatin block. Thanks for posting it. I have seen it many times and am always fascinated by it.

    The Alekseevskii-Tate model can be used to predict not only the maximum terminal penetration depth in 10% ordnance gelatin but also the size of the temporary cavity (using equations derived from the AT pressure-interface equation to model CCE* or SCE** theory), but the math involved is quite complicated making it a bit much to try to post here. What I find mesmerizing are the high frame rate captures of the lead pellets hitting the passing projectiles starting at 2:00 in the video. Those impacts are a brilliant display of how metals flow like water when subjected to the extremely high pressures that occur when metals collide at ordnance velocities. Surprising to most folks unfamiliar to the field is the fact that the viscosity of those flowing metals is only slightly greater than that of water.

    *cylindrical cavity expansion
    **spherical cavity expansion
    ''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.

  2. #12
    ρP(V-U) + YP = ρTU + RT
    α = √[(2√3GT) (2σyT + mρTU)]
    [1 + (ρTU + YT) √(KT - ρTαU)] = YT [1 + (ρTαU 2GT) √(KT - ρTU)]
    and e is Euler's number ≈2.718281828459045

    I was just thinking that.

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