Dr. Kolbe concluded that the maximum rate of barrel rise he documented with his instrumented barrel was just sufficient to achieve positive compensation at 50 yards. There has not been a lot of work done in this area (at least made public) but I have not seen any evidence to the contrary in my shooting. That would be the capacity for my rifle/tuner system to over compensate at 50 yards.
So what can be said of the 100 and 200 yard tuner working, I believe, beyond the effective range of PC. In the first place, they have the potential benefit of all the PC that can be wrung out of the system. And they have an adjustable inertial system to find more or less stable zones of barrel oscillation. Let us back up a bit and think about a weighted barrel vs unweighted or, said another way, a high inertia barrel vs a lower inertia barrel. Note also that the weighted barrel is pre-stressed downward. IMO typical barrel movement is a circular whipping motion with larger vertical excursions than horizontal ... ovoid more than circular actually. If the barrel is pre-stressed into a lower position the oval would have the same or less width but greater vertical. Longer distance shooters bread and butter is dealing with elevation so they may be able to tighten their groups by exploiting tuners in a different dimension than the 50 yards shooter.
This is an a thought provoking way to curate the explanations that have been offered elsewhere for how tuners work.
You suggest that positive compensation (PC) works only about to 50 yards.
At longer distances such as 100 and beyond, however, you say that PC no longer is effective, that PC won't work at distances beyond 50 yards.
(For readers unfamiliar with positive compensation it's an explanation that says tuners work to reduce vertical dispersion by modifying the launch angles of faster and slower rounds in a way that the rounds will have the same POI at a certain distance downrange. This is the basics of Geoffrey Kolbe's work and that of Varmint Al. See, for example,
http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/tuning_a_barrel.htm and
https://www.varmintal.com/a22lr.htm#Two-Flats)
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With regard to PC at 50 yards, when RFBR shooters use carefully selected lots of match ammo they may gain very little from PC. (For the general reader, yes, BR shooters still lot test when using tuners.)
At 50 when ammo ES is under 25 fps and SD figures are very good at under 7 fps, there's little that is gained. A ballistics calculator shows that vertical dispersion between two rounds that are 25 fps apart in MV should be no greater than 0.172". With good ammo it usually much less. The ballistics calculator shows that rounds only 10 fps apart in MV would have a vertical dispersion at 50 yards of 0.080".
In short, with the expected good ammo in use, vertical dispersion because of MV variation can be expected to be quite small. There's not much for tuner-induced PC to do.
Of course, this is not to say that tuners don't work to effect PC or that they don't help at 50 yards. They do, and they make enough of a difference that shooting RFBR without a tuner puts the shooter at a competitive disadvantage. RFBR shooters use tuners because rifles can shoot better
with a properly set tuner than
without.
It's not clear why PC won't work at longer distances. For reducing vertical dispersion alone, it seems that it is at distances of 100 yards and beyond that tuners could have a greater chance to shine.
At 100 yards, for example, the ballistics calculator shows that every 10 fps difference in MV results in about .25" of vertical dispersion. At 200 yards that same 10 fps difference in MV would cause about 1" of vertical dispersion.
Can you elaborate on what you believe it is that tuners do for a barrel at 100 and beyond that they don't do at 50?