I have shot 1000+ registered match targets, burned up 5 barrels, and even taken a few trophies in my work with my Beggs tuner. I devised a way to track and analyze the loads, groups, and tuner performance and I can say definitively that *with a good barrel* I can make predictable, repeatable adjustments to my group sizes at the bench based on largely on temperature and to a lesser degree on humidity. I can also say that I don't hold much stock in most of the tuner discussions I listen in on. Practically every person I know using a tuner is much too coarse in their adjustments, and generally stuck on their notion of how barrels vibrate. This leads to a lot of discussions about weight, in front vs behind the muzzle, and keeping vertical in your groups (sorry Jackie-- but I'll take a flat group every day), but generally doesn't lead to objective results. I shot exactly the same load through most of those targets (for 3 years I never touched my powder measure) and using some basic spreadsheet analysis, came up with a couple simple formulas for adjusting a Beggs tuner that work very reliably between 30 and 95 degrees, and from Raton to St Louis to Phoenix.
Here is my "secret": On the first target of the day keep tweaking the tuner until group is as flat as I can make it - then shoot my record group. On all subsequent targets, do the same.
Keep track of the tuner position (in 1/1000ths of an inch), group size and shape, temperature, and humidity, and (after several hundred groups) you will see a pattern appear. The spreadsheet revealed for my (light by most standards) loads in my LV, it works out to .0012 per degree of temp change. Temp goes up a degree, I move my tuner IN (not out ) by 1.2 marks based on the decal I put on my tuner. This held true across four different barrels -- all of which shot teen aggs at various times. The number is different for my Unlimited gun, but even more stable in its performance. I have an adjustment for humidity changes, but generally don't need it much. I know a few others who correlate both numbers together in a density altitude formula. That works too, but I'm too cheap to spring for a fancy meter when I can do my math on my fingers. (For those with 28tpi Beggs tuners, this is 2 "clock numbers" per 5 degrees temperature).
This formula does not tell you where to start the day -- only how much to "expect" to move the tuner from the "last known good" position. The key is using the tuner to stay exactly on the sweet spot inside a tune node (i.e. the flat group).
There is a lot of good vibration analysis out there, but for me the numbers simply don't work when you extrapolate them to the sensitivity of the tiny tuner adjustments that I know do work. There is a white paper by a long range, live varmint shooter that does correlate to my findings. While he doesn't use tuners, his shock wave pulse models match my tuner analysis for both my LV and UNL guns. Check out Chris Long's paper on Optimal Barrel Time at
http://www.the-long-family.com/OBT_paper.htm. (BTW Chris has some credentials like NASA Fellow Engineer, or something similar-- very bright guy). My synopsis is that tweaking the tuner effectively changes the "length" of the barrel and re-times the position of the shock wave pulse vs. the bullet exit. Small, large, beyond the muzzle or not, wouldn't matter if this is actually the case.
Rod Brown
(Corrected - original post had the tuner going the wrong direction)