u/Lancer-Under-Heaven

I am working up for a trip to Italy this fall, and I am planning to fly into Rome (FCO), but spend a few days in Florence as part of the trip. I am going to Florence via the high-speed train, which means I need to bring the same bag on the train that I fly with.

From what I have read, nothing larger than a carry-on bag will fit in the overhead racks. I am planning to use a 27 inch (Medium-sized) check back: will this have any trouble fitting into the baggage racks at the end of the in the Business-class carriages, or in the between-seat storage?

Additionally - my alternative bag is 31 inches- is this unlikely to fit anywhere the 27 inches bag would fit?

Thanks for the help.