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Thread: Stability of non accelerated flight

  1. #1 Stability of non accelerated flight 
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    I don't belong on this forum with respect to a discussion scenario. But I do need some help. I hope I came to the right place.

    Several of us are experiencing the same results during high power rifle target shooting. It appears to be a long standing phenomenon.

    When firing at targets of different ranges the group size of several shots fired does not increase as expected, with distance. Minute of angle is generally used to describe the expected group size. One M.O.A at 100 yards is roughly a one inch group. All things being equal with respect to weapon, optics, shooter and weather conditions one would expect a group size of roughly 3 inches at 300 yards.

    With regularity the group size does not get larger as expected and in some cases it has been equal at 100 and 300 yards.

    For years the most universal explanation has been that the projectile is not completely stable until some point in it's flight path past 100 yards.

    What I'm looking for is a factual scientific reason. In semi laymanís terms if possible.

    Thanks in advance, I hope I've not been too much trouble.


    Ron
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    This is interesting but I do not understand the set up yet. This group size that you talk about is this from one fingering of the gun or multiple shots from the same gun and person? What is the shape of the projectiles? What is the distribution of the group at the target?


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    O.K., for this question. These are single shots fired by the same person. These guys are competitive long range shooters. It can be assumed that all possible variances that can be controlled have been controlled prior to the bullet leaving the barrel.
    Generally speaking the size of the group of holes in the paper is important. A group can be any number of shots from generally 3 to 10. The equipment, loads, and skill of the shooters is such that any competitor can shoot consistent group sizes repetitively.

    For this problem and if the target at 100 yards has a group of holes measuring 1 inch the rifle is said to be shooting 1 minute of angle. 1 M.O.A. accuracy equates to approximately a 3 inch group at 300 yards.

    In several instances this is not what is occurring. In fact on some occasions with the 100 yard group at 1 inch, the 300 yard group can be as small as 1.5 inches which equates to approximately 1/2 M.O.A. The rifle is shooting more accurate farther down range.

    This occurs with spitzer (pointed) bullets that have either a flat base or a boat tail (tapered) base. It usually occurs in boat tail bullets at farther distances due to its higher ballistic coefficient of friction. If it's any help these projectiles are spinning at the rate of twist of a particular rifle however a rate of one revolution per 12 inches would be normal. A normal bullet speed exiting the barrel is around 3000 fps.

    Given the fact that the bullet is pitching and yawing as soon as it exits the barrel and spinning really fast the theory is those radical movements settle down out past 100 yards or so and the bullet becomes more stable in flight.

    The question is why does it do that?
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  5. #4  
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    why do say the bullet is pitching and yawing?
    bullet rpm=V(1/T) 60 , T is twist in inches, V in fps thus a 2200 fps bullet is spinning at 132000 rpm for a 12 inch twist. that's the gyro stabiliztion effect .

    furthermore you leave out that the shooter is compensating for the drop with range.
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  6. #5  
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    I do apologize for leaving out the bullet drop part. Actually it doesn't make any difference. The concern here is not where the group of projectiles are hitting the paper but rather the size of the group on the paper.

    Below is a quote from barrel maker Gale McMillan. He is long dead. It may explain my question better than I

    The difference in muzzle velocity between rounds causes the bullets to
    go through the paper at close range at different points of the
    spiril. You will see this more frequently as time goes by due to the
    numbers of tight twist barrels being used in this fad of shooting overly
    heavy, long bullets. Shoot a 55 grain bullet out of a 9 twist barrel
    etc. There has been posts in this thread indicating that the dispersion
    of shots would be in seconds and minutes of angle proportionate to the
    distance checked. Then I ask why not check every thing at short range
    and eliminate shooter error. We shot 18000 rounds of 50 cal ammo during
    a contract. The guns were sighted in and function tested at 100 yards
    and averaged 1.5 moa groups. When these same guns were tested at 600
    yards you would expect the groups to run 1.5 moa or 9 inches. The 600
    yard targets ran as small as 3 inches and never any larger than 6 inches
    as an average. Any that shot larger than 9 inches were inspected and re
    tested.

    Gale McMillan
    Ron
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    I'm thinking about the relationship of the image the shooter ses in the scope to the group size.

    I assume the shooter is using some kind of magnifying scope.
    Does the shooter up the magnification when the target is farther away?
    For instance, does the shooter double the magnification when going from a 100 yard target to a 200 yard target?
    Does the shooter then increase the magnification by another 50% to go from 200 to 300 yards?

    Your answer will determine if my idea has any validity.
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    I think I know where you are going. This group size that gets smaller than anticipated happens to almost all competitive shooters. There are all manner of scopes being used from high power fixed, i.e. 24x, 36x etc. to every variable known. Most variable power scope shooters do not change the power at different ranges. Variable power scopes arenít used much in this game anyway. The clincher is it happens to Palma shooters and they are using metal receiver sights. No scopes allowed.
    Ron
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  9. #8 Re: Stability of non accelerated flight 
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    Quote Originally Posted by win71
    I don't belong on this forum with respect to a discussion scenario. But I do need some help. I hope I came to the right place.

    Several of us are experiencing the same results during high power rifle target shooting. It appears to be a long standing phenomenon.

    When firing at targets of different ranges the group size of several shots fired does not increase as expected, with distance. Minute of angle is generally used to describe the expected group size. One M.O.A at 100 yards is roughly a one inch group. All things being equal with respect to weapon, optics, shooter and weather conditions one would expect a group size of roughly 3 inches at 300 yards.

    With regularity the group size does not get larger as expected and in some cases it has been equal at 100 and 300 yards.

    For years the most universal explanation has been that the projectile is not completely stable until some point in it's flight path past 100 yards.

    What I'm looking for is a factual scientific reason. In semi laymanís terms if possible.

    Thanks in advance, I hope I've not been too much trouble.

    I suspect that what you are seeing is a fluke.

    If the dispersion were simple angular dispersion then you would expect it to be linear -- one inch at 100 yards opening to 3 inches at 300 yards.

    But it is not linear. It is much worse.

    You are correct in that a bullet is much like a spinning top and there is pitch and yaw to be considered. There is tip-off at the muzzle, which is minimized by a uniform muzzle crown to make the interaction between the bullet and the propellant gasses symmetric at exit, but will not be zero. There is probably also some damping of the precessing motion as the bullet goes downrange, but any assymetric launch conditions will have alread done their damage and the bullet will not return to the "nominal" flight path once it has started to deviate, so there is no benefit in increased range in reducing group size.

    There is also the matter of cross wiinds and bullet drop. Bullet drop , as you know is a very nonliner function of time of flight, which is dependent on velocity. So variability in velocity translates to vertical dispersion and the effect is more pronounced with increasing range. Crosswind effects are also dependent on time of flight and get worse with increasing range, although the effect is more pronounced withe crosswinds near the muzzle than nearer the target. In any case range would only make the windage effect greater with increasing range.

    There is at least one effect that might, on a given day, but not over the long haul, reslt in what you have seen. One is differing crosswinds over the course of fire. It is nust possible, for instance, that a slight west wind near the point of fire is compensated by a slight east wind nearer the target. There are also often time-of-day differences in wind conditions at some shooting facilities that might favor an earlier or later event.

    Are you using the same loads, or ammo from the same lot, at all rnages ? Is the forearm supported in the same way ? Is it possible that your barrel is susceptable to some fouling and the barrel is in a different state for the two events ? Is is possible that you are more nervous earlier in the match, or more fatigued later one and that affects the targets at one range more than the other ?
    Are wind conditions the same for the two ranges ? Are your rates of fire the same (which would affect barrel heating) ?

    Are you shooting 5.56 mm or 7.62 mm ?
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  10. #9  
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    win71 says it occurs to all shooters in different environments, and the quote he posted shows that they have tested it under fixed conditions. i dont understand how it can be described as fluke, unless i have misinterpreted something.

    i think the gyro stablisation effect may be along the right lines. If you think of the bullet when it leaves the barrel, its flight path will be unstable at the beginning. It will pitch and yaw, not randomly, but will oscillate back and forth. when viewed straight on its flight path will look like a spiral with a radius that reduces over distance as the bullet becomes more stable due to the gyro stablisation. so the distribution size for 10 shots on a target would be like the cross section of a cone that gets smaller with the distance of the target (until shooter accuracy becomes relevant).

    perhaps the higher MOA at the start is due to the target being within an area where the radius of the unstable flight path is larger, and over distance the bullet becomes more stable. the fact that the flight path oscillates then it will cancel out so that the bullet actually has more chance of hitting a smaller group size then if the target was closer to the gun.

    I can visualize the problem, but im finding it difficult to explain in a post.
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  11. #10  
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    My first idea clearly does not apply.

    So now Iím thinking harvestein has it right. Once the bullet stops tumbling, gyro stabilization would cause it to oscillate a bit. Then throw in air resistance to reduce the magnitude of the oscillation and that could explain the observed behavior.

    If that was the case, a (small) rocket launched into the air would behave the same way. Do we have any rocket scientists in the group?
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  12. #11  
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    mikelizzi i actually meant that the fact that the bullet is spinning would reduce the oscillation in its flight path over time, but i didnt word it very well.

    i think the oscillation in the bullets flight path when first fired is actually caused by the fact that the bullet doesnt come cleanly out of the barrell. It tends to have rattled around slightly on its way out so the bullet does not come out pointing perfectly in the direction of its trajectory.

    then thats when the aerodynamics and gyroscopic action would kick in to stablize the spiralling motion (caused by bullet not being centered on it trajectory) into a straighter flight path.
    What i meant by 'cancelling out' was that the imperfect flight path (spiral) averages out over distance so that the bullet ends up closer to the centre point of the spiral (I.E. where the shooter was pointing the gun), but i just re-read this line, and i think im just explaining the word 'spiral' in a different way. got to love fridays.....

    Some slow-mo cameras would be good!
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  13. #12  
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    Quote Originally Posted by harvestein
    mikelizzi i actually meant that the fact that the bullet is spinning would reduce the oscillation in its flight path over time, but i didnt word it very well.

    i think the oscillation in the bullets flight path when first fired is actually caused by the fact that the bullet doesnt come cleanly out of the barrell. It tends to have rattled around slightly on its way out so the bullet does not come out pointing perfectly in the direction of its trajectory.

    There is no oscillation in the flight path of the bullet, just pitch and yaw about the center of gravity. A bullet does not "porpoise". The pitch and yaw oscillations may dampen out due to aerodynamics, but that does not mean that the trajectory is some sort of camped sinusoid about a "true" trajectory that would result in lower group size with increased range.

    The bullet most certainly does not "rattle around" in the barrel. In fact the fit is very tight, and the bullet is deformed to engage the rifling. There is, as noted some initial disturbance due to gas dynamics at the muzzle, but that is not due to any rattling around in the barrel. There can be effects if the bullet does enter the throat symmetrically, but that is an ammunition effect that has nothing to do with range. It is often handled by seating the bullet so as to engage or nearly engage the rifling when the shell is chambered.
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  14. #13  
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    Quote Originally Posted by harvestein
    Some slow-mo cameras would be good!
    Or a laser pointing closely parallel to bullet path, with sensor at the other end. You could catch this undocumented "porpoising" in the breaks.
    A pong by any other name is still a pong. -williampinn
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  15. #14 Thanks 
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    Appreciate the easy to understand explanation by harvestein.
    Ron
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  16. #15 Re: Thanks 
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    Quote Originally Posted by win71
    Appreciate the easy to understand explanation by harvestein.
    Unfortunately it is wrong. That is quite common with easy-to-understand answers to complex questions.

    You will find, unfortunately, that even among many professionals there is a general lack of science applied to small arms. The situation is very much better for medium caliber and large caliber ammunition. Fortunately some of that is now carrying over to the small arms arena, slowly, largely because of acquisition of small arms companies by people with experience, expertise and analytical capability built in the medium and large caliber arena.
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  17. #16  
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    Seems harvestein described a phenomenon that DrRocket says should not be considered in bullets... so DrRocket is the one perhaps simplifying a complex problem... though I think he'd admit it does occur in some other projectiles? Arrow, darts, etc. Why are bullets in particular simply unaffected?
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  18. #17  
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    Quote Originally Posted by Pong
    Seems harvestein described a phenomenon that DrRocket says should not be considered in bullets... so DrRocket is the one perhaps simplifying a complex problem... though I think he'd admit it does occur in some other projectiles? Arrow, darts, etc. Why are bullets in particular simply unaffected?
    Beacuse bullets are spin stabilized and not aerodynamically stabilized. Arros and darts have fins and are stabilized by the center of pressure being in back of the center of gravity.

    I must admit that I am not familiar with firearms. I have not fired one in nearly 5 hours, and it has been a few years since I was responsible for development of new ammunition for military applications.
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    While I was over here someone over there (where the original discussion began ) came up with a reference that almost seems to make sense. Thanks again for the responses here..........

    http://www.the-long-family.com/bullet_dispersions.htm
    Ron
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  20. #19  
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    Quote Originally Posted by win71
    While I was over here someone over there (where the original discussion began ) came up with a reference that almost seems to make sense. Thanks again for the responses here..........

    http://www.the-long-family.com/bullet_dispersions.htm
    That does not begin to explain equal absolute group sizes at 100 and 300 yards, or even 1.0 vs 1.5 inches. It also assumes that the dynamics of barrel motion (vibration) are perfectly consistent, which we know is not the case, since among other things that would require perfectly consistent internal ballistics.
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    Third Try: (What? Iím learning.)

    I still want to give the OP the benefit or the doubt and assume the grouping phenomenon he describes is real. And I still do not believe that the gyroscopic motion of a bullet, by itself, could be responsible for it. In that regard I am in agreement with Dr. Rocket. My reason is that gyroscopic motion only affects the rotation of an object. It does not, cannot affect its translation. And the phenomenon the OP is describing has to do with translation, an apparent correction to translation in flight.

    So am I saying rifling does not correct accuracy? Am I now contradicting a basic tenant of weapons design? I hope not. Thatís why I brought up the issue of aerodynamic drag. It seems to me that the coupling of gyroscopic motion and aerodynamic drag must be what makes a spinning bullet more accurate.

    I put together a crude analysis which suggests how that could happen. The web page may be viewed at the following URL.

    http://mysite.verizon.net/mikelizzi/...bilization.htm
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  22. #21  
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    Quote Originally Posted by mikelizzi
    Third Try: (What? Iím learning.)

    I still want to give the OP the benefit or the doubt and assume the grouping phenomenon he describes is real. And I still do not believe that the gyroscopic motion of a bullet, by itself, could be responsible for it. In that regard I am in agreement with Dr. Rocket. My reason is that gyroscopic motion only affects the rotation of an object. It does not, cannot affect its translation. And the phenomenon the OP is describing has to do with translation, an apparent correction to translation in flight.

    So am I saying rifling does not correct accuracy? Am I now contradicting a basic tenant of weapons design? I hope not. Thatís why I brought up the issue of aerodynamic drag. It seems to me that the coupling of gyroscopic motion and aerodynamic drag must be what makes a spinning bullet more accurate.

    I put together a crude analysis which suggests how that could happen. The web page may be viewed at the following URL.

    http://mysite.verizon.net/mikelizzi/...bilization.htm
    Rifling causes a bullet to be "stable" in flight through the atomosphere. If the bullet is not stable, if it tumbles, then aerodynamics forces quickly cause extremely erratic flight -- so erratic that you could not hit a pie plate at 25 yards with a rifle ( been there done that).

    If there were no atmosphere, then rifling would make no diffrence and an bullet would follow a perfectly predictable parabolic arc, even if it were to tumble in the process. Accuracy would be greatly enhanced if the effect of the atomosphere could be eliminated.

    It is not simple aerodynamic drag, in the usual sense of the word, that is at work. Drag in the normal sense would only affect the speed of the bullet, but not have any other effect llike lift). The detailed aerodynamics of a real bullet in flight is very complex -- you are dealing with supesonic flow of a compressible gas over a solid body and the body is perhaps changing orientation with respect to the velocity vector. Because of the complexity of the problem, exterior ballistics is usually done with much simplified empirical models, and not with fundamental fluid dynamics.
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    Dr. Rocket,
    What have I said this time that you disagree with?

    You said "Rifling causes a bullet to be "stable" in flight through the atmosphere." My analysis assumes that too.

    You said "If there were no atmosphere, then rifling would make no difference" Well Duh...

    You said "It is not simple aerodynamic drag" Well, I called my analysis crude. I do not pretend to understand the complexity of air-bullet interactions under supersonic conditions. But the general conclusion that air and spin together contribute to a more accurate path still applies. No?

    What more do you want?
    Do you think a 20 page treatise with sophisticated equations would help the original poster?
    Did you want me to include some deference to the experts in ballistics?
    OK. If I need a gun designed I promise to ask for help and not try and do it myself.
    Anything else you would like me to do?
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  24. #23  
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    Quote Originally Posted by mikelizzi

    What more do you want?
    I would be nice if your analysis and your posts addressed the important aspects of the physics of the problem. They don't. Your analysis as your site misses the main point completely. In fact it in no way even addresses the effect of spin and rifling.

    What you have is a simplified model of nominal bullet drop, which is basically irrelevant to the issue of dispersion, and dispersion is the phenomena addressed in the OP.

    The effect of rifling is to stabilize the bullet and to keep it from tumbling. When a bullet tumbles the effect on accuracy to make the point of impact totally unpredictable, even within a matter of many feet at, say, 100 yards.



    Quote Originally Posted by mikelizzi
    Do you think a 20 page treatise with sophisticated equations would help the original poster?
    It might. Treatises like that have been written and have proved valuable in the past. It would rather depend on his level of sophistication in physics. It would certainly help you to understand the physics better.

    Quote Originally Posted by mikelizzi
    Did you want me to include some deference to the experts in ballistics?
    You could. Better yet you might try reading some of their stuff yourself. Chapter VI, "Motion of a Rotating Projectile" in Methods of Exterior Ballistics by Forest Ray Moulton is pretty good.

    Quote Originally Posted by mikelizzi
    OK. If I need a gun designed I promise to ask for help and not try and do it myself.
    Given the analysis at the site that you linked that is probably a good idea.

    Quote Originally Posted by mikelizzi
    Anything else you would like me to do?
    You might develop a capability to learn and not have such a thin skin.
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    Dr rocket you may disagree with my suggestion, but you have not explained an alternative.

    when i said oscillates i mean that the bullet pitches and yaws back and forth, not randomly, it is predictable and is repeating. thats why i used that word. you seem to think the flight path will be very erratic, which is not so. If you watch a bullet in slow motion you will see what i mean. In fact i though one of the other posters reference to a dart was quite helpful. Im referring to the same type of pitch and yaw motion.

    i didnt mean the bullet would some how magically find its way to where the shooter is pointing, i said the probability increases with distance.

    "rattle around" is a loose term, i was trying to illustrate that the bullet does not come out pointing aerodynamically centered on its trajectory therfore its flight path will take a circular deviation if viewed straight on, that will eventually diminish.

    I still feel my explanation is still valid, you have tried to bin the whole thing by using vague statements without actually providing something for me to reconsider. Despite your sarcastic confidence about your experience with firearms, you are not being helpful to the discussion.

    I would like you to explian this sentence:
    " It also assumes that the dynamics of barrel motion (vibration) are perfectly consistent, which we know is not the case, since among other things that would require perfectly consistent internal ballistics."
    in greater detail as i do not understand how this requires perfect consistency in regards to the vibrations in the barrell, if anything a vibrating barrell would be in favour of my explanation of bullets being off-center when they exit. It also contradicts what you said earlier about bullets not rattling around (for want of a better terminology).

    Also please explain or elaborate on this sentence:
    "Unfortunately it is wrong."
    Why is it wrong?

    You also said-
    "That is quite common with easy-to-understand answers to complex questions. "
    I find it strange you said this when it was you that suggested the shooter was the cause (perhaps he forgot his lunch?) or the wind, or size of bullet. The basis of the question and referenced experiment rules that out.
    but then you would know that, wouldnt you? being so experienced in firearms.

    Thanks for your input though.
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    can i also point out this sentence is false:
    "Beacuse bullets are spin stabilized and not aerodynamically stabilized"
    rifle bullets are both. if it wasnt aerodynamically stable, then it wouldnt be stable atall would it.

    Also i just read the article that win71 posted and it describes perfectly what i was trying to illustrate, just put a much better way than i:

    http://www.the-long-family.com/bullet_dispersions.htm

    Forget 'oscillation' this guy uses "Epicyclic Swerve", i like that much better.

    Forget 'spiral paths' this guy uses "helical path", more accurate description.

    Although id like to see what his reasoning is for the assertion that the helical path stays constant and doesnt diminish.

    Ive also just had a look around on different web pages and it seems that I am not the only one who has offered something like this as the most likely explanation. Although with added bells and whistles.

    Nice to see that i wasnt going off in a world of my own after all!

    Rant over, better get back to work......
    'Aint no thing like a chicken wing'
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  27. #26  
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    Go get a copy of "Hatchers Notebook" an excellent referrence on ballistics.
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  28. #27  
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    Quote Originally Posted by harvestein
    can i also point out this sentence is false:
    "Beacuse bullets are spin stabilized and not aerodynamically stabilized"
    rifle bullets are both. if it wasnt aerodynamically stable, then it wouldnt be stable atall would it.

    Also i just read the article that win71 posted and it describes perfectly what i was trying to illustrate, just put a much better way than i:

    http://www.the-long-family.com/bullet_dispersions.htm

    Forget 'oscillation' this guy uses "Epicyclic Swerve", i like that much better.

    Forget 'spiral paths' this guy uses "helical path", more accurate description.

    Although id like to see what his reasoning is for the assertion that the helical path stays constant and doesnt diminish.

    Ive also just had a look around on different web pages and it seems that I am not the only one who has offered something like this as the most likely explanation. Although with added bells and whistles.

    Nice to see that i wasnt going off in a world of my own after all!

    Rant over, better get back to work......
    wrong

    There is a great deal of utter nonsense published in the gun world. Don't rely on anyting other than solid analytical treatises, complete with all relevant equations.
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  29. #28  
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    Quote Originally Posted by DrRocket
    Don't rely on anyting other than solid analytical treatises, complete with all relevant equations.
    I prefer empirical data. Apparently this question needs experiment.
    A pong by any other name is still a pong. -williampinn
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  30. #29  
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    Quote Originally Posted by Pong
    Quote Originally Posted by DrRocket
    Don't rely on anyting other than solid analytical treatises, complete with all relevant equations.
    I prefer empirical data. Apparently this question needs experiment.
    For some things you need empirical data.

    But this thread started with apparently inexplicable empirical data.

    At that point you need some solid theory.

    It exists, but it is rather complicated. The problem is the motion of an unconstrained spinning rigid body, subject to gravity and aerodynamic forces.

    Moreover, the problem is the dispersion on the trajectory of that body, given variabliliy in initial conditions.

    It is a rather complex problem and is not treated very well in the popular literature. For instance mikelizze find comfort in the popular literature supporting his "analysis" but if one looks at that "analysis' you find no modeling of the gyroscopic effects of spin or of aerodynanic forces other that simple drag, aligned with the velocity vector. That has NOTHING to do with dispersion, unless one takes into accoutn variability in initial conditions and his analysis simply ignores variability in its entirety.
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    Dr rocket, its all very well saying im 'wrong' and there is lotsof 'nonsense' writtenabout guns.

    Please explain why im wrong, this is the third time i have asked?

    You are very good at writing long paragraphs without actually saying anything.
    'Aint no thing like a chicken wing'
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  32. #31  
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    Quote Originally Posted by harvestein
    Dr rocket, its all very well saying im 'wrong' and there is lotsof 'nonsense' writtenabout guns.

    Please explain why im wrong, this is the third time i have asked?

    You are very good at writing long paragraphs without actually saying anything.

    Then read the posts and think a wee bit.

    Bullets are stabilized by spin and are not stabilized aerodynamically like arrows. If they were aerodynamically stable we would not need rifling. Also, the twist rate would not be so critical as it is. If you have ever see the result of a bullet that does not properly engage the rifling you would know just how aerodynamically unstable a bullet can be -- they can go through a paper target sideways even at close range.

    Further look at the purporyted "analysis" which claims to explain the effect of spin yet includes no physics that is result of spin. That make the claim completely ridiculous.

    Now, don't expenct me or anyone else to learn classical mechanics for you. A valid reference has been provided in this thread -- real physics complete with the applicable differential equations. Go read it.

    That fact that you don't understand a post is not synonymous with lack of content n the post.

    Bullets do not rattle down the barrel. They in fact deform and obturate. There is important variatility in the dynamical response the of the gun and particularly the barrel in relation to the stock and action while the bullet is in the barrel -- which relates to variability in initiial contitions and is sometimes molified with the use of barrel tuners (as in some Browning rifles). There is also a gas dynamics effect at exit which is very complex, but can be molified by the geometry of the barrel crown.

    There is a big difference between questins affecting the mean impact point of a bullet, and the dispersion about that mean. It is the dispersion that is the issue raided by the OP. There are very large number of interrelated factors involved.

    Now, quite reading the nunk in the popular magazines and web pages and go read one of the few treatments of exterior ballistics that is based on actual physics. See earlier reference.
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  33. #32  
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    Quote Originally Posted by win71

    This occurs with spitzer (pointed) bullets that have either a flat base or a boat tail (tapered) base. It usually occurs in boat tail bullets at farther distances due to its higher ballistic coefficient of friction. If it's any help these projectiles are spinning at the rate of twist of a particular rifle however a rate of one revolution per 12 inches would be normal. A normal bullet speed exiting the barrel is around 3000 fps.

    Given the fact that the bullet is pitching and yawing as soon as it exits the barrel and spinning really fast the theory is those radical movements settle down out past 100 yards or so and the bullet becomes more stable in flight.

    The question is why does it do that?
    This is pretty close to correct. However, the reason is in the way atmospheric drag works. Basically, there is a cruising speed for a bullet as it rips through the atmosphere. It has to slow down to that speed before its path will become stable. So, it has less to do with spin, and more to do with the atmosphere simply exerting less drag.

    This is the equation.

    http://en.wikipedia.org/wiki/Drag_%28physics%29




    F is the force of drag,
    P is the density of the fluid,[3]
    V is the speed of the object relative to the fluid,
    A is the reference area,
    C_d is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car), and
    The weird V is the unit vector indicating the direction of the velocity (the negative sign indicating the drag is opposite to that of velocity).

    A, C_d, and P don't change much during flight. The bullet's drag properties, and the air's thickness are pretty much just constants. The weird v is just to describe the direction it's traveling in, and it's not terribly important either because the drag will be about the same no matter what direction the bullet is traveling in.

    The thing that does change is the bullet's velocity, V. Initially, right out of the barrel, when it's going really really fast, it's experiencing a lot of drag. Since velocity is squared in the equation, that means it isn't just experiencing a little bit more drag when it's going fast. It's experiencing exponentially more drag. Once the bullet slows down to its cruising speed, that drag will have diminished to the point where it's much more acceptable, and that should mean that the bullet's path remains more stable.

    I'm going to post one more link that could be fun to read. It turns out that the cruising speed for bullets in water is so low that they're not even lethal. And, because water is thicker than air, they reach that speed much more rapidly than they do in air. I think it only takes about 14 feet.

    http://kwc.org/mythbusters/2005/07/m...oof_water.html
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  34. #33  
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    Quote Originally Posted by kojax
    Quote Originally Posted by win71

    This occurs with spitzer (pointed) bullets that have either a flat base or a boat tail (tapered) base. It usually occurs in boat tail bullets at farther distances due to its higher ballistic coefficient of friction. If it's any help these projectiles are spinning at the rate of twist of a particular rifle however a rate of one revolution per 12 inches would be normal. A normal bullet speed exiting the barrel is around 3000 fps.

    Given the fact that the bullet is pitching and yawing as soon as it exits the barrel and spinning really fast the theory is those radical movements settle down out past 100 yards or so and the bullet becomes more stable in flight.

    The question is why does it do that?
    This is pretty close to correct. However, the reason is in the way atmospheric drag works. Basically, there is a cruising speed for a bullet as it rips through the atmosphere. It has to slow down to that speed before its path will become stable. So, it has less to do with spin, and more to do with the atmosphere simply exerting less drag.

    This is the equation.

    http://en.wikipedia.org/wiki/Drag_%28physics%29




    F is the force of drag,
    P is the density of the fluid,[3]
    V is the speed of the object relative to the fluid,
    A is the reference area,
    C_d is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car), and
    The weird V is the unit vector indicating the direction of the velocity (the negative sign indicating the drag is opposite to that of velocity).

    A, C_d, and P don't change much during flight. The bullet's drag properties, and the air's thickness are pretty much just constants. The weird v is just to describe the direction it's traveling in, and it's not terribly important either because the drag will be about the same no matter what direction the bullet is traveling in.

    The thing that does change is the bullet's velocity, V. Initially, right out of the barrel, when it's going really really fast, it's experiencing a lot of drag. Since velocity is squared in the equation, that means it isn't just experiencing a little bit more drag when it's going fast. It's experiencing exponentially more drag. Once the bullet slows down to its cruising speed, that drag will have diminished to the point where it's much more acceptable, and that should mean that the bullet's path remains more stable.

    I'm going to post one more link that could be fun to read. It turns out that the cruising speed for bullets in water is so low that they're not even lethal. And, because water is thicker than air, they reach that speed much more rapidly than they do in air. I think it only takes about 14 feet.

    http://kwc.org/mythbusters/2005/07/m...oof_water.html
    Your statement regarding a bullet cruising speed and stability of a trajectory is just plain wrong. What is true is that the coefficient of drag peaks near mach 1., decreases beyond that and essentially "plateaus" for large mach numbers.

    If a bullet is unstable as it leaves the barrel, it typically does not "settle down" but rather tumbles with a completely unpredictable trajectory.

    The sort of trajectory that you are describing applies to aerodynamically stablilized projedtiles, like arrows, but not to most bullets. Arrow leave the bow with not only pitch and yaw , but also with an elastically deformed shaft (look up "archer's parados") and that elastic behaviour of the arrow does damp out and result in straighter flight (at least of the arrow head). That is why arrow penetration typically increases with distance for a short period following launch.

    The equation describing the drag is correct. However the drag coefficient is dependent on the mach number (not speed, but the two are directy correlated so long as the temperature of the atomosphere is constant over the trajectory) and is somewhat variable depending on the speed regime involved. Cd, plotted as a function of Mach number exhibits a very large change near the speed of sound (the so-called transsonic region). If you have bullets that go from supersonic to subsonic, the change in Cd can be pronounced. This would be the case with, for instance, high velocity .22 rinfire or larger calibers at long distances.
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  35. #34  
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    Quote Originally Posted by DrRocket

    Your statement regarding a bullet cruising speed and stability of a trajectory is just plain wrong. What is true is that the coefficient of drag peaks near mach 1., decreases beyond that and essentially "plateaus" for large mach numbers.

    I totally forgot about the fact that bullets travel at supersonic speed. That surely does change everything, doesn't it?

    Also, I was trying to keep it simple. In reality, even arrows don't exactly have a "cruising speed" but the drag gets less the slower they go.

    The sort of trajectory that you are describing applies to aerodynamically stablilized projedtiles, like arrows, but not to most bullets. Arrow leave the bow with not only pitch and yaw , but also with an elastically deformed shaft (look up "archer's parados") and that elastic behaviour of the arrow does damp out and result in straighter flight (at least of the arrow head). That is why arrow penetration typically increases with distance for a short period following launch.
    Yeah. Arrows are exactly what I was thinking of.
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  36. #35  
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    Quote Originally Posted by kojax


    I totally forgot about the fact that bullets travel at supersonic speed. That surely does change everything, doesn't it?

    Also, I was trying to keep it simple. In reality, even arrows don't exactly have a "cruising speed" but the drag gets less the slower they go.
    One problem with the questoin as originally posed is that the phenomena involved are not simple.

    Exterior ballistics at the level required to address issues of dispersion of bullets is rather complicated. What you have is a spinning projectile that is not aerodynamically stable without spin, that may not be perfectly symmetric, launched from a barrel with asymmetric initial conditions and which also involves the dymanics of the gun and barrel. There are a lot ot effects and they are of varying levels of importance. The most important effects with regard to dispersion (not the overal trajectory but dispersion) are due to "junp" effects at the muzzle and dynamics of the barrelgun vibrator modes and pretty much dwarf everything else, assuming tha the bullet has sufficient spin to be stable.
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  37. #36  
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    I have to say this is the part that's really interesting. I wonder if there's a human component. Maybe the fact the target actually looks smaller from a distance motivates the shooter to aim more carefully in order to be assured of hitting it?

    Quote Originally Posted by win71

    For this problem and if the target at 100 yards has a group of holes measuring 1 inch the rifle is said to be shooting 1 minute of angle. 1 M.O.A. accuracy equates to approximately a 3 inch group at 300 yards.

    In several instances this is not what is occurring. In fact on some occasions with the 100 yard group at 1 inch, the 300 yard group can be as small as 1.5 inches which equates to approximately 1/2 M.O.A. The rifle is shooting more accurate farther down range.

    I can't think of any good physics reason why a bullet that's off by 1 M.O.A. at 100 yards would self correct in order to be at only 1/2 M.O.A. at 300 yards. Not unless there were some kind of spiraling effect.

    I'm pretty sure I've seen a football throw or two that had a spiraling effect like that, where it kind of self corrects over time into a stable spin, but I have to admit I have no idea whether bullets are capable of doing that. Gyroscopic effects are subject to wind resistance just like any other component of an object's velocity, which means that the total angular momentum should be changing during flight, so it wouldn't surprise me if something were happening there.
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