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I have a crazy idea. If a barrel is ground oval shaped after the chamber area. Would it vibrate in one plane instead of something like a figure eight or something more complex. If it vibrated in one plane it would be easier to tune. It would be interesting if someone tried it.
 
possible-barrel-contour.png

THE TWO-FLATS CONTOUR.... The barrel in front of the action is 1.25" in diameter and tapers down to 1.1" in diameter at 4" from the action. From there, the barrel diameter is 1" and the distance between the flats is 0.643". The muzzle is 1" diameter for 2 inches so a tuner could be used. It is 24.75" long. The flats start at 4.5" and extend to 22.25". At each end of the flats, the transition is 0.5" in length. This contour allows for more vertical flexibility in the vertical direction than a 1" full diameter barrel. But it has nearly the same stiffness in the horizontal direction as a 1" diameter barrel.

There is more info on this barrel contour on my 22LR page:

http://www.varmintal.com/a22lr.htm

It calculation shows an upward muzzle projection for a wide range of velocities and preserves nearly the same horizontal stiffness of the 1" diameter barrel. I don't have the facilities to actually make the barrel in real hardware.
 
That would be the VTR. They shoot extremely well. As a matter of fact it shot(.308) better than my 700VS in .308. We got 3/8 th's inch groups with federal hi-shok ammo which is their cheapest load. It also shot 168 grain match bullets well.
 

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