Here is a note about shotgun barrel length, you might find helpful. I don't know how well it was researched, but I expect the source to have some knowledge...
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
Here is a link to many questions on shotgun chokes, barrel length velocitys, shot size, etc. Might find some of it interesting.
http://www.guncustomizing.com/tech.htm