Online, oblaze will probably not find much in the way of meaningful information. In the period of 1985 through 1995 lots of information was being published on muzzleloading firearms. One such publication was "The Gun Digest Blackpowder Loading Manual" published in 1995. It contained good information and topics on the care and use of muzzleloading firearms. Specifically there were tables that detailed the performance of 768 loads for 156 blackpowder rifles. There were traditional rifles in percussion and flint along with some in-line rifles and a few black powder cartridge rifles.
Presently the Fourth Edition of the manual is in print and can be found online. It will have the same information as in the Third Edition, which I have and added information primarily on modern muzzle loaders.
Other than the old Lyman Black Powder Manual that all sorts of tables for muzzle velocity and trajectory for various lengths of barrels, there is some specific information on loads and little formulas to provide the % increases based on barrel length and powder to apply to a rifle one would have in their possession.
Few examples are in the Third Edition. Most rifles are half stock in 50 caliber and most long rifles are in 32, 36, or 45. I did find two rifles in 50 caliber, the 1816 Remington and the Mountain State Mountaineer. Both had barrel lengths of 39" and shot round ball of 0.490" diameter using a 100 grain volume measure of FFg GOEX (at that time branded as GOI) powder. Muzzle velocity of the Mountaineer was 1921 feet per Second and the Remington was 1926 feet per second. A representative half stock with a 34" barrel, The New Model Ithaca Hawken using the same round ball and 110 grains volume of FFG GOEX had a muzzle velocity of 1912 feet per second. A Thompson Center Hawken rifle with a 28" barrel had a muzzle velocity of 1456 feet per second. The Lyman Deerstalker with a barrel of 24" using 80 grains of FFG had a muzzle velocity of 1301 feet per second. They didn't use 100 grains of powder in the shorter barrels. One last entry for the Green Mountain drop in 32" barrel using 100 grains of FFG GOEX had a muzzle velocity of 1809 feet per second.
The conclusion is that longer barrels will have more muzzle velocity. The percent change will depend on ball diameter, patch thickness, patch lubrication and quality of the powder.
The loading manuals can be found. The Fourth Edition of 2003 is out there. 20 year old information is better than none, I suppose.
https://www.amazon.com/Gun-Digest-B...k+powder+loading+manual&qid=1698756125&sr=8-4