Well fatter barrels ar stiffer so the heavier (meaning conture) the stiffer they are the stiffer they are they move less when shot (barrel harmonics)
All barrels "flex" or "vibrate" or "bow" when the bullet passes through it due to the extream pressure and force of the bullet beinbg shoved through it at very high speed and RPM. Heavy barrel also take longer (more rounds)to heat up so getting an accurate 5-10 shot group is easier with a realy heavy barrel than a very thin one. This is not saying that you can't have a thin barrel shoot as accurately as a heavy barrel but it would shoot as accurately for as many shots.
As for the barrel length , their are to things to look at ,
#1 the longer the barrel the higher velocity it will allow , this is especialy true with bigger cased-overbore guns like the mag and Ultra mags
#2 the longer the barrel the less stiff it is so you have to find a point of deminishing returns for your needs , theirs no sense in having a 30" barrel for a 6mmPPC cause its not needed to get optimum accurate velocity , like wise it woulden't make alot of sense to have a 20" full bull barrel on a 7mmRUM thats your gonna be carrying around the mountains.
So if your looking for an ultra accurate gun thats gonna be shot from the bench only them big oversized and full bull barrels are ok but if your building a elk rifle to pack 10hrs a day through the mountains you don't want it to weigh 25lbs so you must sacrifce the ability to shoot a tight 5-10 shot group (generaly not needed anyway) for a lighter weight barrel.
One other thing that I'm sure is gonna come up is barrel fluting. Some people are told that "fluting a barrel makes it stiffer" this is completly wrong , their is no way you can have a solid cylinder that must be a certain length that will withstand X amount of force then remove material and that make it stiffer. So if you have a #8 conture barrel then have it fluted it will not be stiffer than it was before BUT if you use a #8 barrel and flute it so that is weighs the same as a #6 barrel then you will have a barrel that is stiffer than the #6 yet weighs the same.
Another reason to flute a barrel , and the main one in my oppinion , is to increase surface area , the more surface area that is available to the open air the faster the barrel will cool down.
So if you want a rilfe that weighs 9lbs with a #6 barrel but you want a stiffer barrel you can either
#1 get a fatter barrel and have it fluted
#2 cut the #6 barrel shorter those making it stiffer
Their are down sides to each of those , and they are that fluting a barrel is not cheap and cutting a barrel shorter makes you give up some velocity so you have to give somthing.
I personaly like fluted barrel just because I like the look , if it offered zero benifit I'd still probably have a few rifles with fluted barrels.
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