What are rules of thumb for designing a gravity feed system for cylinders?

So, I just printed out this battery holder off Thingaverse. Unfortunately, it doesn’t work very well, so I’m interested in redesigning it. There’s a number of issues but the most annoying one is that the batteries keep getting stuck and not gravity feeding like they are supposed to, forcing you to shake the holder or reach up the output slot to bump the batteries until they feed out again.

The reason is obviously that the holder is just a box and that the cylindrical batteries jam up against each other at the bottom where the downward motion suddenly becomes horizontal.

A quick perusal of things like soda vending machines and ammo feed mechanisms shows that a v-shaped feed mechanism seems to be the standard way of doing this correctly.

However, I have no idea what sort of convergence angle and other considerations need to be made for designing such a device. I could made a tall, slowly converging angle, but that makes the storage box a lot taller and lower capacity than is idea. Too sharp of a convergence angle and I’ll have the same jamming issues found in the existing design.

So, I assume that there is some sort of literature out there for designing feed systems for cylindrical objects. Obviously, things like cylinder density, surface roughness and other factors will affect this, but I assume that there’s at least some sort of rough rule of thumb out there for what the optimal shape should be – e.g.: 45 degree convergence angle + some factor * the cylinder W/L ratio, etc.

I know I can figure this out with Edisonian trial and error, but I really don’t feel like burning up a bunch of PLA and time if there’s a decent standard rule of thumb I can use as a starting point for experimentation.