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Importance of bedding/floating?

What are the key principles of bedding/mounting a barrel to maximize accuracy? As I understand it now you just don't want anything touching the barrel that can vary shot to shot, whether that's a sandbag or a fore-grip in the hand of a shooter.

I have seen long barrels that are pillar-bedded near the breach, and float over the stock from that point. And equally-accurate barrels that are glass-bedded the length of the stock. So it seems that a heavy barrel doesn't have to be supported along its length to be accurate?

Now suppose we have a very long, unbalanced barrel: Is there any way to support the fore-end of a breech-mounted barrel -- e.g., on a bipod mounted on rails welded to the barrel -- that can preserve accuracy? Or is a second point of contact always going to adversely impact accuracy?
 
You want the rifle to vibrate the same way each time it is fired. The easiest way to do that is to free float the entire barrel. Anywhere the barrel touches anything there is the potential for inconsistency in that contact.

A requirement for consistent barrel vibration is to have the stock firmly attached to the action. There are several ways to do this, the most common being to attach it via pillar bedding for reasons given here:

http://bisonballistics.com/articles/rifle-action-screws-torque-accuracy-and-bedding-issues

I'm not sure why you'd want to support the muzzle - how long is the barrel anyhow? I suppose in theory, you could come up with a way to do that, but unless you're talking about a rail gun, you're better off just letting it float.
 
If you are talking about a really long, heavy barrel, you can use a barrel block to mount the barrelled action to the stock. That way there is plenty of support for the barrel and yet is floated. Not real popular, but one option.
 

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