I mean that if the ID of the tube is effectively infinite, pulling the filament through the tube is no different from dragging it across the floor, in which case, the only force contributing to friction is from gravity. The filament’s bend radius will only attempt to conform to the tube’s bend radius if the filament is flexible enough to collapse under its own weight (plus whatever amount of force is pulling it taught, which depends on the resistance at the other end).
But you mean aside from the capstan friction from the tube’s large-scale curvature, right? That’s seriously where most of the drag comes from. Try pulling filament through a straight 4x2 tube and compare to the same tube with a couple loops in it.
Does that still apply to a filament that is too stiff to conform to that curvature? The tube should have a larger natural bend radius than the filament. It seems to me that until the tension is sufficient to make the bend radii match at the contact surfaces, you will instead have point contacts, and the angular term of the capstan equation will be essentially zero.
Dunno about 3mm filament, but it doesn’t take much tension (maybe a half pound at most) to get 1.75mm filament to reasonably conform to any reasonable tube curvature. The exact contact shape doesn’t matter, it’s the normal force at the circumferential contact required to react against the tension vectors at the free ends of the line that generates the capstan friction. (Again, Coulomb friction only depends on normal force, not contact area or pressure.)
I think line stiffness can only add to the capstan friction. If you imagine the filament curvature naturally matches the large-scale bend of the tube, that’s equivalent to a non-stiff line and only capstan friction will occur. If you then make the filament curvature different from the tube (tighter or looser), there is still the same normal force due to tension at the free ends of the line, but it also has an additional force component of the filament and tube trying to deflect each other.
Half a pound sounds like a lot to me. The ideal spool holder will have nearly zero dynamic friction, only enough to keep the filament from unspooling itself due to the bending force of wrapping it around the spool.
If you just shove a stick through the center of the spool, then yes, I can see how capstan friction would come into play, at least with 1.75.