Many of us hunters and shooters hear a lot about "floating," "free floating," or "pressure bedding" rifle barrels, "bedding" the action, "glass bedding" the barrel, and such as that. What does it all mean, and how might it be helpful to you? Such questions are simple and complex at once, because rifles are often as individual as people - but the basics are easy to explain. Most of these methods are employed almost exclusively on bolt-action rifles.
Floating (or free floating) a rifle's barrel means isolating it from everything forward of the chamber (rear) portion of the barrel. Basically, the only parts of the barreled action (which consists of the receiver and barrel as a unit) that touch the stock are the receiver and the fatter chamber portion of the barrel - everything forward of the chamber is free-floating, and touches nothing.
Why float a barrel? Well, when a rifle barrel heats up due to the high temperatures resulting from firing a cartridge, the metal naturally expands. Pressure on various points along its length from high spots in the stock's barrel channel can cause the barrel to bend ever so slightly as it heats up, which naturally may cause bullets to fly someplace other than where the previous shot(s) went.
Since a floated barrel doesn't touch the stock along its length, that variable is removed from the equation. Sometimes it works to improve repeatable accuracy, and sometimes it doesn't. Floating is at its best when used with rifles that have relatively heavy (large diameter) "bull" barrels, because they are less flexible than slimmer barrels. Lighter "sporter" barrels are less stable, and may flex enough during the shot that accuracy will suffer.
Pressure bedding is usually a form of floating. Remington uses a form of this on their Model 700 rifles - usually leaving a built-up portion of the stock in the barrel channel which applies pressure to the bottom of the barrel at the front end of the forearm, but otherwise the barrel is floated. Sometimes this works well, and sometimes it doesn't.
When shooting a Remington M700 in 222 Rem, I was very pleased at the accuracy of the rifle and the cartridge - but only out of a cold barrel. As the barrel heated, groups would open wide. A close inspection showed that the build-up at the fore-end was very large - so large that with it there, the forward action screw could not be tightened fully. The barreled action was in firm contact with the stock only at the rear of the action and the front end of the stock.
I attacked the build-up with sandpaper, and removed it completely. When I was done, I had free-floated the barrel and could tighten both action screws thoroughly, gaining firm contact between stock and receiver, with the barrel touching no part of the stock forward of the chamber. I happily headed to the range, hoping that I had cured my rifle of sucking eggs.
I had not.
The rifle still strung shots as the barrel heated, same as before. I decided to try a method I'd seen mentioned in a book called "Make it Accurate," which involves trying varying amounts of pressure against the barrel at different points, until accuracy is improved. In my case, this meant cutting a piece of a business card and adding it as a shim under the barrel at the fore-end - where the huge build-up of wood had been when it came from the factory. Bingo! She settled right down and started acting like the accurate rifle that I knew she could be. The pressure-bedding idea that Remington had used was the right idea, but in this case it had been poorly implemented at the factory.
Pressure bedding can be used in rifles other than bolt-actions, too. The book mentioned above talks about using a small shim under the barrel located roughly midway between the receiver and barrel screw to improve the accuracy of a single-shot rifle.