Pretty sure that gambrel, or 'barn' roofs, were designed for hay storage...hay lofts.
They actually had soffit vents.
Now they are just a 'cute fad' for sheds and houses.
The main reason for big roof overhangs is to have soffit ventilation.
Top hinged windows will keep most rain from coming in thru windows.
There's no way to estimate eave depth to deter rain infiltration thru/on the wall,
depends on how the wind blows.
Make them a big as you can.