Gain Twist is a form of rifling popularized by the famous barrel maker, Harry Pope, back in the 1970s, and '80s. The twist starts slowly at the breech or throat of the gun barrel, and the rate of twist speeds up until the bullet leaves the muzzle. Gain twist was NOT used with PRB. Its was intended and used in shooting bullets- and paper patched bullets at that.
Harry believes that the sudden explosion and overcoming of the inertia of the bullet as it sat in the chamber, or breech of the barrel cause the bullet lead to skid as it tried to gain velocity, in effect cutting the outer edge of the bullet, and destroying the gas sealing fit of bullet to barrel on the rifling lands. Later, when hard cast bullets and copper jacketed bullets were used, it became clear that this was not the case, no matter how fast a ROT is used and how fast the bullet is traveling down the barrel. Part of the reason for this NOT happening has to do with some laws of physics which were not understood at the time Pope was doing his work.
For our purpose, visualize a bullet in a barrel at the moment the powder ignites and gases start pushhing on the bullet. The impact of the gases on the bottom, or backend of the bullet will cause the bullet to distort in shape, driving part of the metal sideways into the grooves until the grooves are filled, and will take no more metal. ( in paper patched lead bullets, its the paper that is shoved sideways into the grooves.)
From that point on all the added gas pressure put on the base of the bullet pushes the bullet down the barrel, and out, with the bullet gaining velocity rapidly, while in the barrel. We have all seen enough rocket launches to be able to visualize what is happening to that bullet in the barrel once it begins to move. Motion is expotential, once the inertia is overcome. Its only when the bullet leaves the barrel and the gases no longer can push on the back of the bullet that the bullet begins to lose velocity.
Gain twist was actually adopted for the Italian Carcano rifle in 1891, when the 6.5 x 52 mm Mannlicher Carcano cartridge was adopted by that country. Its is the only military rifle which ever used the gain twist system, and it was also the first smokeless power military cartridge adopted by any country. Pope, and obviously, the Italian government, thought that the gain twist would make their cartridge shoot flatter and farther. All the 6.5 MM cartridges are good flat shooters, even at the modest velocities of these old war dogs, but it has more to do with the long skinny bullets that have extraordinary Ballistics Coefficients, that give the calibers their reputations for long range accuracy and killing power, than anything
" gain twist " contributes to the mystique!
If you are shooting a single shot BP cartridge gun, or a bench gun that uses a false muzzle to load the bullets, then you can use paper patching to protect the bullets from the bore, and rifling, and THEN, you can consider if Gain Twist is something you might want to fool with.
There is a barrel maker that has figured out Harry Pope's Code, and can make gain twist barrels in all the old Pope calibers. There was an article about him more than 20 years ago in Muzzle Blasts. I have forgotten his name, but I am sure I saved the article some place.
Perhaps John Hinnant will comment on this question, as John has spent as much or more time chasing down old techniques as anyone now living in the USA.