Shotguns burn their powder pretty quickly, some of it actually makes excellent magnum pistol powder.
This is part of why muzzle brakes don't work all that well.
Mid brakes are the hot ticket on shotguns.
Remington is often quoted on the internet as saying the powder is burned between 12 and 14 inches.
That is incorrect.
What they actually say is 13"-16" and max velocity is achieved by 20".
Remington
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Will a longer shotgun barrel shoot farther?
Modern smokeless powders burn in the first 13 to 16 inches of the barrel and maximum velocities are obtained in the first 20 inches.
Shot will carry the same distance regardless of the barrel length.
Shot pattern will be the same whether the barrel is 21 inches in length or 30 inches in length, if the barrel has the same choke constriction.
Our experts state there would be a small variation in velocity when using a 21-inch barrel as compared with a 30-inch barrel; however, the variation would be immeasurable.
The basic advantage of a shorter barrel is that it will swing faster.
The longer barrel gives the hunter a longer sight radius to be more precise, particularly when pass shooting waterfowl.
Also, the longer barrel can often help balance certain shotguns better.
http://remington.custhelp.com/app/answers/detail/a_id/51/kw/Shotgun pattern barrel length/r_id/166
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What you could do is get a short barrel with an adjustable choke.
That way you could tune the spread to your liking.
At defensive ranges I would be willing to bet there won't be enough difference between 12" and 18" to matter.
Watch this video and see what you think.
http://americangundog.com/movies/AGD1-E3_SS_l.html
Here is something from the Browning Fac
**Snip**
It is still assumed by many that the longer the shotgun barrel the farther the gun will shoot, the more effectively it will perform, and the more closely it will pattern. The facts are, however, whatever the gauge, barrel length has small effect on the velocity of the shot charge. With modern powders, the shot charge reaches maximum velocity after it has traveled a relatively short distance up the barrel bore. (So longer length of barrel does not make the pellets move faster or go farther.) Since the degree of choke controls the pattern of the shot at the target, proper barrel length is entirely a matter of desired weight, balance, and sight radius.
~ Source: Browning FAC
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I am going to Quote Jerry Pardue and Tony Rumore now.
Jerry Pardue
**Snip**
Barrel Length
It is still assumed by many that the longer the shotgun barrel the farther the gun will shoot, the more effectively it will perform, and the more closely it will pattern.
The facts are, however, whatever the gauge, barrel length has small effect on the velocity of the shot charge. With modern powders, the shot charge reaches maximum velocity after it has traveled a relatively short distance up the barrel bore. (Longer length of barrel does not make the pellets move faster or go farther.) Since the degree of choke controls the pattern of the shot at the target the proper barrel length is entirely a matter of desired weight, balance, and sight radius. The longer 30 or 32 inch barrels add weight at the muzzle for steadiness, and provide a longer sighting plane for the slower, more deliberate swing required to hit more distant targets. The shorter barrels are preferred whenever quickness in getting a gun shouldered, and general ease of maneuverability, are important.
The size of the individual is also a consideration. A small person will likely be more accurate, even for distant targets, with a shorter barrel since the longer barrel may be uncomfortably heavy and slow.
**Snip**
Tony Rumore with a quote from Jason Hinkle
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This was posted by Jason Hinkle over on Subguns. Jason got me into the Saiga market back in 2004 and owns the very first prototype 12" Tromix SBS. He's a pretty colorful guy.......
Hinkle writes......
OK so I finally took most of the shotguns out for a spin on the old Chronograph. What I found is that, basically, those of you chuckleheads with no empirical data who have been yapping your cockholsters about how short barrels on shotguns seriously affect ballistics are fucking wrong. Lots of wrong. Like I said long ago, shotgun powder IS pistol powder- it burns fast and quick, and barrel length doesn't fucking matter that much.
I can't .PDF a spreadsheet on this computer so I'll get really slow and dumb like those who talk out their ass about ballistics with no basis in reality and list the average FPS for the shot strings.
First, using shitass birdshot- 12 gauge, 2 3/4 inches, 1 oz shot
12" barrel average FPS- 1040
14" barrel average FPS- 1069
18" barrel average FPS- 1114
19.5" barrel average FPS- 1114
20" barrel average FPS- 1108
28" barrel average FPS- 1159
Then using Remington 00 Buck-
12" barrel average FPS- 1121
14" barrel average FPS- 1127
18" barrel average FPS- 1216
19.5" barrel average FPS- 1205
20" barrel average FPS- 1182
28" barrel average FPS- 1250
Wow- 119-129 FPS velocity loss in 16 inches of barrel. That's devastating. Oh wait- no, it's actually not, it's fucking nothing at all and is actually about the same velocity variation in factory loaded ammo. I will feel as comfortable fucking up a bear using a shotgun with a 12 inch barrel as I would using one with a 28 inch barrel. Those of you clammering over 20 gauge Serbu Super Shortys rather than the biting sting of a 12 gauge to dust up a gravel pit should stick with the shortest of shotshells. I wouldn't want you to drop your purse while shooting.
**Snip**
Shot patterns produced using the same
12-gauge shotgun with shotshells
containing #4 shot pellets
Courtesy of Jack Dillon
http://www.ojp.usdoj.gov/nij/training/firearms-training/module12/fir_m12_t06_12.htm
If you have read this far you ought to go ahead and click these links.
You may find just the factoid you are looking for.
http://firearmsid.com/A_distshotpatt.htm
http://www.myscienceproject.org/shooting.html
http://americangundog.com/straightshooting.html