Really ? I'm sure I have seen them run upside down on lathes.
I can't 100% remember, but I seem to recall someone running it right side up, and over time had wore some grooves in their flat pulley, from the grooves in belt riding in the same location continuous. But I truly don't recall the details.
On engines, you have crank, fan, alternator, and tensioner at minimum. So contact area for each pulley is smaller. Assuming a lathe with just two pulleys, that would be close to 75% contact area per pulley. I would guess that's enough grip, but I have not personally gone this route on anything.
On grooved side, the grooves do matter though. Grooves on grooved pulleys will wear to the extent, that even with a new belt, the belt/pulley will squeal, and need replacement pully. And/or the grooves on pulley become sharp, and belt sinks into it, getting sliced along each groove.
South Benders do it both ways. Some also cut the belts and lace them, Some cut the belts and glue them.
I don't understand any of that.
1959-60, we were taught to skive a taper into the LEATHER flat belt and glue it with ignorant hide glue.
It was never a problem in need of any other solution but the OEM leather belt one. Some folks just have a compulsion to outsmart themselves by making easy things harder.
SB's have typically 3/4 HP or less, max, use only a fraction of it.
The serpentines used are typically rated 5 HP or better in long-serving and severe underhood environment automotive use. Rib-count thing. They only MAKE one width, over a meter wide.
The rest is done by a "slitter" making-up various widths out of the raw "master" band stock at each given hoop diameter/length.
One popular fine-grove family is rated about .41 HP per rib. More power = more rib-count = wider belt. Published information. That simple.
I can't imagine an SB's miniscule loading wearing one of proper width out before the lathe itself is worn clear to flinders. Even the OEM leather belts last for long years.
SB's are light lathes. VERY light.
5 HP air compressor, (Dayton // El Cheapo)? Those I HAVE seen wear-out serpentine belts and shiney-wood pulleys.
CI - or the steel ones automotive uses? Not so much and not so fast.
If ANY of them are wearing sharpish? That's from slip. annnnnd ..
We are back to the door we came in through.
The pulley is too small in diameter for the loading. Or not WIDE enough for the loading and diameter.