Transonic Cone Theory of Bullet Motion

TacticalDillhole

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  • Jun 26, 2012
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    Well there you go, I don’t have the litz books handy. I guess all that is left is to convert radians per second to rpm’s but I’m not convinced that’s the right formula and at a minimum doesn’t tell the whole story.

    Also that white paper is for artillery and requires the installation of a sensor on the shell to measure the inertia. I’m not sure it applies to small arms projectiles at this time.
     
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    Secant

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    Well there you go, I don’t have the litz books handy. I guess all that is left is to convert radians per second to rpm’s but I’m not convinced that’s the right formula and at a minimum doesn’t tell the whole story.

    Also that white paper is for artillery and requires the installation of a sensor on the shell to measure the inertia. I’m not sure it applies to small arms projectiles at this time.
    Yep, for artillery. Physics isn't really going to vary from artillery to bullets from a big picture perspective, so I would expect an exponential rotational decay for bullets as well. Don't take this the wrong way, but unless you are able to write and solve the appropriate differential equations, I wouldn't worry about getting too far into the weeds. If you have the appropriate background in kinetics, kinematics, fluid mechanics, etc., then by all means, go nuts.

    And for whatever it's worth, I 100% agree that projectiles are not course correcting mid-flight. I don't follow as to how the bullet's position relative to max ord plays any role. I see it as a time-of-flight issue. The greater the amount of time of unstable or less-stable flight corresponds to greater unpredictability/inconsistency.
     

    TacticalDillhole

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    Yep, for artillery. Physics isn't really going to vary from artillery to bullets from a big picture perspective, so I would expect an exponential rotational decay for bullets as well. Don't take this the wrong way, but unless you are able to write and solve the appropriate differential equations, I wouldn't worry about getting too far into the weeds. If you have the appropriate background in kinetics, kinematics, fluid mechanics, etc., then by all means, go nuts.

    And for whatever it's worth, I 100% agree that projectiles are not course correcting mid-flight. I don't follow as to how the bullet's position relative to max ord plays any role. I see it as a time-of-flight issue. The greater the amount of time of unstable or less-stable flight corresponds to greater unpredictability/inconsistency.
    The max ord thing is just a thought. I’m not spouting it as fact or theory. I just think of it in terms of its pitch and yaw as it travels up before it begins to descend. There could very well have no basis in fact. I’m not a ballistician. But if it reaches transonic before it starts to come down you compound the effects defeating gravity with a now unstable projectile is it’s still trying to reach that ord before it descends I just think it’s worse than it happening when it hits that point when it’s already on it’s way down. It may act more “predictably” in that situation.
     

    lowlight

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    image.jpeg

    You can see it's off center


    Once they start cavitating it's over, this was so predictable every video I shot was a success, I never missed a bullet coming apart

     

    timintx

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    Ok still tracking …just going to chop it up a few times because there is a mix of testing and theory inside

    Also, there will be a bunch of questions that may cross between theory and proprietary info, so answer what you can without “slipping”..dont want to cause trouble if you have other entities involved.

    So previously you had seen 2 out of 10 “bullet trace” look different in flight but they were still in a tight group, but you didn’t have a reason/theory yet.


    During testing for positive compensation:

    From what I had always read positive compensation only really showed up at distance because the trajectory difference of velocity at 100 was almost impossible to separate from possible bullet irregularities and environmentals.

    I know short range BR guys dont even weigh powder, they volume dump at the bench because velocity differences don’t really show up.

    How did you induce the variables for the 100 yard testing, different charge, seating depths?

    Were you able to compensate for those “standards”, and bring the POI inside/tight which is actually “outside” the expected groups from those different loads?

    Im thinking if several loads expected POI partially overlap then its luck of the draw/ possible if they converge to the same POI even without compensation?


    Modifying patterns..:

    What or how much positive compensation had you been seeing at 100, or better yet what velocity differences were you using/ targeting as your variables (I would think the weapon, components, location, POA, etc are the static variables).

    The suppressor was the right weight…:

    That must be a formula; I have not seen a calculation for a tuner weight which in theory is what the suppressor is acting like…as you suggest it “should be tuned” or im off base?

    I would think that calculation includes, barrel material, barrel length, bore size, OD, profile at a minimum.

    Is the suppressor a clip on or a screw on?

    If the suppressor should be of correct weight, you also must have calculated the exact position of the suppressor when attached as the exact location is part of setting up a tuner.

    If the exact attachment point is calculated, was the suppressor able to be “moved” fore and aft for tuning?

    I’d think with the tuners on the market that adjust/move a few .001”s when adjusting.. how was that accomplished or the suppressor was designed with best case scenario and load development was “going to bring it home”?


    Downrange:

    So, after the suppressor killed your dreams at 100 (lol) you shot it farther (1000) and the instead of the groups being 30” / 3MOA they were tac driving..with suppressor on correct?

    Did you try the same ammo at 1k without suppressor for a quick base line of what the rifle and load could actually do?

    Would be great to know if the load/rifle was capable of “clay bird” at 1k without suppressor, then we would know suppressors effect at 1k, if nothing else.


    Final design:

    You believe that by redesign you have made a “proper” suppressor which has limited effects on accuracy compared to the original un-suppressed rifle or that’s still on going


    Sorry if long winded, trying to make it so I can follow your answers properly and not ask doubles.


    Thanks

    edit..ill check spelling AGAIN a little later..Iphone
    May be best to answer these questions on another thread , I dont want to detract from the original post.
     
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    Anyone have any theories how doppler radar isn’t able to pick up bullets spiraling with a wider radius and ending with a smaller?
     

    Mike Casselton

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    The term is laminar not laminate. And eventually it becomes a turbulent zone and that’s what creates the twist

    What do you know? You just fly airplanes... 🤣🤣

    To add to this discussion, if you've ever watched an aircraft takeoff in high humidity conditions you can see the effects of laminar flow.

    And yes, the flow can and will oscillate without the aircraft wobbling, corkscrewing or any other control issue.

    So many people have little to zero understanding of wind effects on projectile flight.
    Spend some time watching sensitive wind flags and how tiny changes affect point of impact and flight characteristics.
     

    TacticalDillhole

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    What do you know? You just fly airplanes... 🤣🤣

    To add to this discussion, if you've ever watched an aircraft takeoff in high humidity conditions you can see the effects of laminar flow.

    And yes, the flow can and will oscillate without the aircraft wobbling, corkscrewing or any other control issue.

    So many people have little to zero understanding of wind effects on projectile flight.
    Spend some time watching sensitive wind flags and how tiny changes affect point of impact and flight characteristics.
    FE328574-A466-4444-9EFB-8A344A649802.jpeg
     

    TacticalDillhole

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    Anyone have any theories how doppler radar isn’t able to pick up bullets spiraling with a wider radius and ending with a smaller?
    because doppler doesnt detect rotation like that. it measures velocity as an object moves towards or away or in the case of weather detection, it can take a vertical cross section and detect wind speed and direction because its picking up on the particles in the air.
     

    Feniks Technologies

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    because doppler doesnt detect rotation like that. it measures velocity as an object moves towards or away or in the case of weather detection, it can take a vertical cross section and detect wind speed and direction because its picking up on the particles in the air.

    It wasn’t a serious question. Just making a point. Lol
     

    Jim Boatright

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    Just out of the muzzle, the initial spin-rate ω0 of the bullet in radians/second is given by:

    ω0 = 2π*V0/Tw = 2π*12*V0/(n*d)
    where V0 is the muzzle velocity in feet/second, the twist rate Tw is given in feet/turn, n is the number of calibers/turn, and d is the caliber in inches.

    Thereafter, the spin-rate ω(t) of the bullet slowly decays almost exponentially with time of flight t (in seconds), so that

    ω(t) ≈ ω0*exp[-(0.0321/d))*t]

    where the caliber d is given in inches. This formulation was suggested by Dr Geoffrey Kolbe in England.

    The numerical coefficient in the exponential (in units of inches per second) comes from analysis of PRODAS spin-rate data for several different 30-caliber military rifle bullets out to 900 yards. The exponential expression is about a 1-percent fit to the PRODAS aerodynamic data.

    Doppler radar tracking of projectiles fired for maximum range DOES show the damped coning motion of spin-stabilized projectiles during the descending limb of their long-range flights. You can measure the remaining coning rates directly from the modulated velocity plots.
     
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    timintx

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    Just out of the muzzle, the initial spin-rate ω0 of the bullet in radians/second is given by:

    ω0 = 2π*V0/Tw = 2π*12*V0/(n*d)
    where V0 is the muzzle velocity in feet/second, the twist rate Tw is given in feet/turn, n is the number of calibers/turn, and d is the caliber in inches.

    Thereafter, the spin-rate ω(t) of the bullet slowly decays almost exponentially with time of flight t (in seconds), so that

    ω(t) ≈ ω0*exp[-(0.0321/d))*t]

    where the caliber d is given in inches. This formulation was suggested by Dr Geoffrey Kolbe in England.

    The numerical coefficient in the exponential (in units of inches per second) comes from analysis of PRODAS spin-rate data for several different 30-caliber military rifle bullets out to 900 yards. The exponential expression is about a 1-percent fit to the PRODAS aerodynamic data.

    Doppler radar tracking of projectiles fired for maximum range DOES show the damped coning motion of spin-stabilized projectiles during the descending limb of their long-range flights. You can measure the remaining coning rates directly from the modulated velocity plots.
    Thank you Jim for clearing that up . This explains what I have seen in my testing.
     
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    357Max

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    Just out of the muzzle, the initial spin-rate ω0 of the bullet in radians/second is given by:

    ω0 = 2π*V0/Tw = 2π*12*V0/(n*d)
    where V0 is the muzzle velocity in feet/second, the twist rate Tw is given in feet/turn, n is the number of calibers/turn, and d is the caliber in inches.

    Thereafter, the spin-rate ω(t) of the bullet slowly decays almost exponentially with time of flight t (in seconds), so that

    ω(t) ≈ ω0*exp[-(0.0321/d))*t]

    where the caliber d is given in inches. This formulation was suggested by Dr Geoffrey Kolbe in England.

    The numerical coefficient in the exponential (in units of inches per second) comes from analysis of PRODAS spin-rate data for several different 30-caliber military rifle bullets out to 900 yards. The exponential expression is about a 1-percent fit to the PRODAS aerodynamic data.

    Doppler radar tracking of projectiles fired for maximum range DOES show the damped coning motion of spin-stabilized projectiles during the descending limb of their long-range flights. You can measure the remaining coning rates directly from the modulated velocity plots.
    Does this formula account for sectional density?
    I’m no mathematician, but my instinct is telling me a long Mono will spin decay much quicker than a traditional lead core of same shape.

    I’ve kicked around the idea that a jacketed Anviloy ® projectile could improve small caliber performance at ELR ranges. Of course this would be an AP round & wouldn’t play well with steel. Probably be fine at a mile+ with .224
     

    Jim Boatright

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    Your feeling that that bullets having smaller axial inertia values would spin-decay faster is correct, Max, all else being equal. Where you are mistaken is in thinking this would be a large effect. The radius of gyration (kx) of a bullet about its spin-axis varies much more with caliber and overall "bullet" shape than it varies with any reasonable differences in non-homogeneous material densities. The axial moment of inertia (Ix) is given as m*(d*kx)^2, where m is the mass of the projectile and kx is given in calibers (d). "Depleted" uranium is the highest density core material available and makes the heaviest projectiles available in any given caliber. They no doubt have very long spin-decay time constants.

    The formulation I gave is for existing military style jacketed, lead-alloy cored 30-caliber rifle bullets. Artillery projectiles, for example, all have much lower sectional densities than rifle bullets, but only slightly faster spin-decay rates reflected in their slightly smaller exponential time constants after adjusting for caliber difference.
     
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