It seems every sling bullet from antiquity is bioconicsl or almond-shaped. When a sling bullet is traveling through the air, does it spin about the long axis, like an American football? Or does roll around the long axis? Or...how does it travel through the air?
They’re shaped to reduce drag, and made of heavy material like lead so they really drill through the air and deliver max energy to the target.
I have a bit of experience slinging. My thought is that the shape allows for the projectile to leave the sling pocket in a fairly repeatable orientation thus eliminating one of the many variables that affect accuracy. Achieving accuracy when throwing, slinging, shooting, hurling, tossing, or chucking is a matter of practice and eliminating variables, i.e. grip, distance, sight alignment, breathing, consistent projectile weight, shape, powder charge, warhead weight, number of windups, etc. Quarterbacks throw the football only one way so the toss is predictable. Pitchers throw unpredictably with myriad variables to confuse.
Check out this guy slinging:
https://youtu.be/RzDMCVdPwnE