How did muzzle-loaded rifled artillery solve the problems of the hand-held rifle?

The answer lies in the age-old conundrum: how to muzzle-load a firearm whose bullet is supposed to tightly engage with the barrel. I'll rewind back to the 1700s and work up how rifles worked to get to your question.

The normal infantry weapon of many years was the smoothbore musket. It was rather easy to use: the ball was usually under-sized to the bore, so it would go right in. Since ammunition was not really standard, you could get balls with a looser or tighter fit. When fired, the ball would go plunk-plunk-plunk down the barrel and depart in the vague direction of the muzzle at a fairly high speed. The system could withstand a bit of variation in its use, including in what all items were loaded into the barrel, ball sizes, and so on.

A rifle was much more difficult to work with. One of the issues was how to get the tight-fitting ball down the barrel. One solution was to use a full-bore ball and whack it into the muzzle with a mallet, which formed the bullet to the rifling, then continue running it down with the ramrod, yet being very careful to stop ramming it once it meets the powder (you did not want to smash black powder). In old paintings of rifle skirmishers from the 1700s, you might see them with a mallet in their belt: then you know that they were using full-bore balls and reloading took some work.

Another solution was to use a slightly undersized ball and wrap it in a material (like greased cloth or a sabot of leather or even wood). This made the ramming process softer and faster, but the engagement of the ball to the rifling bands was not as tight.

The challenges with old rifles required someone who knew what they were doing. A cold barrel would have to be warmed in order to get balls into it. Too much powder and the soft lead bullet would strip off the bands and not get spun. Since the ball encountered a LOT of friction in the barrel compared to the smoothbore, it had a lower muzzle velocity. It was still more accurate, but the slower muzzle velocity forced the soldier to work with a pronounced ballistic path.

In the early 1800s, specifically around 1830-1850, efforts were made to get better performance out of muzzle loading rifles to the point where they could be a regular line weapon and not just a specialist weapon. Most of this work was in France. Louis-Etienne de Thouvenin figured that by putting a peg at the breech, you could drop an under-sized ball down the barrel, then use the ramrod to smash the ball on the end of the peg. The goal was to deform the ball (like into a mushroom shape) so that its soft lead would engage the rifling when fired. The peg was sized so that the powder charge would be around its base, thereby preventing the smashing process from abusing the black powder. Henri-Gustave Delvigne was also working with aerodynamically-shaped balls in addition to concepts about the loading problem, and so there was the desire for combining these attributes. Sabots - a "carriage" that would run the bullet down the barrel and then drop away - were experimented with but didn't seem to reach mass use (the exception being a sabot of greased cloth or paper, which was very commonly done).

This eventually evolved into the classic Minie bullet (named after Claude-Etienne Minie): an aerodynamic bullet with a chamber in the back, a system that was largely figured out by 1850. The bullet was under-sized to the bore, but when fired, the back of the bullet would flare and engage the rifling. This might be considered a type of driving band, which is a band that engages the rifling while the rest of the bullet/shell does not. Even if you look at a modern NATO 155 mm shell, you'll see the copper driving band that goes around it, which is the only part of the shell that engages the rifling (the body of the shell does not engage the rifling).

Taking the concept to muzzle-loading artillery, obviously one can't put in a full-bore shell and count on hammering it in - you'd be applying a lot of abuse to a shell loaded with powder and with a fuse on the front. It's going to have to be an under-bore shell that slides in, and then when fired somehow engages the rifling on its outbound journey. The answer was in a variety of sabots and driving bands, with concepts mostly similar to their hand-held counterparts:

• Parrot Rifles used a typical-looking aerodynamic shell with a fuse on the front. The back end of the shell had a lead band around it with a small chamber formed as a result. The firing of the charge would expand the driving band out to engage the rifling. It's kind of like a Minie solution.
• The James Rifle shell, also an aerodynamic design, had a cage on the back with lead panels. When fired, the panels would be blown outward to engage the rifling. This might be called a kind of sabot, at least in a loose definition of the term.

Some good reading about this topic in regards to small arms (but not artillery - although the concepts are similar):

The Destroying Angel: The Rifle-Musket as the First Modern Infantry Weapon (2018) ISBN 978-1719857277 by Brett Gibbons.

The English Cartridge: Pattern 1853 Rifle-Musket Ammunition (2022) ISBN 979-8645988975 by Brett Gibbons.