I am well aware of Bryan's testing in regards to non linear dispersion. I have signed copies of all of his books because I think that his work is incredibly valuable.
I do not own any rifles that exhibit non linear dispersion. I did not claim that and as such lack the neccessary tool to accept Bryans challenge.
What I will say is that I have personally experienced many 1000 yard benchrest competitors with rifles that shoot poorly (think .75 moa) at 100 yards, but consistently shoot the same rifle/load at 600 in the .4 range, and in the .5-.6 range at 1000. Seemed like an appropriate way of answering Euros question.
My own short range benchrest rifle (100,200,300) will shoot results that mimic the Benchrest Results that Bryan used from one of the Supershoots (at least if I am not having a shitty day). As that rifle is not used to compete at ranges past 300 I have not had reason to shoot it farther.
There is no question that this phenomenon is at least perceived to exist. I have been following his (Bryan) threads on sites like longrangehunting in regards to this matter because I am excited to see the eventual conclusion.
As of this point I still believe that the point at which a bullet achieves its greatest stability during its flight directly affects its ability to "buck the wind". There is always air moving between your muzzle and the target, and depending on that distance, the part of a bullets flight where it is least stable will have the greatest affect on its ultimate trajectory.
Does this ideally explain the idea of non linear trajectories? No, not really. At least not to me.
That said, something, somewhere, has caused some rifles to group better at long range than they do at short range. If it were just something I had heard then I would discount the phenomenon. That I have seen it in person, from skilled shooters, leads me to believe that something is causing it. The current thinking is that it is in regards to "the bullet going to sleep" and I answered Euro as such.
It may not be the bullet/rifle/load at all. It could ultimately be a mental issue, as was one of the more prevalent ideas offered up in this regard.
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