Artillery shells a stabilised by rifling. Grooves in the barrel that spin the round up as it exits by digging into the outside of the round.
This is great, but it has two problems.
The first is that it stabilises the shell to the orientation of the barrel, not the direction of flight. Fine if you are engaging a target roughly in line with where you are aiming, but if you are shooting almost directly up, the shell will come down *backwards*. Fins stabilise to the direction of travel.
The second problem is that it takes a lot of force to engage the rifling. Fine for a breach loaded shell that only engages the rifling while being forced out by the propellant charge, but mortar shells are fired by dropping them into the barrel and letting them slide down. Muzzle loading a rifled barrel requires a ram rod, which if you used on a mortar would mean that the first thing the mortar hit would be the person firing it.
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