It seems intuitive to roll a print to image to the inside. But, this stresses the inkjet receptor coating more so than rolling it to the outside. However, rolling the image to the outside perplexes the customer when they receive it. What we do at Cone Editions Press when we do not ship flat is to roll the print to the inside of a 5" core tube that we purchase from yazoo mills. We slip sheet it with archival tissue. Roll it. Use a slip sheet outer wrapper which is taped. Then this gets bagged in an archival poly bag from Universal Produts. This goes into the tube with some room around its diameter so the customer does not damage it trying to pull it out. We use some bubble wrap for cushioning on the ends and the tubes come with 5" plastic end caps which we tape closed. We use archival materials in case the customer decides to leave it wrapped up forever. Without all the archival wrapping the cardboard will stain the paper in just a few months.
For the 40" I would get the 5" x 48" tubes.
With a 5" core, there is much less stress to the inkjet coating and the inks and GO which are adhering to the coating. We haven’t tried shipping in anything less than 5" since forever - so we can’t say if using something smaller will affect the coating. For shipping flat we buy triple thick cardboard sheets from Uline. The prints are slips sheeted and bagged. Then it is taped securely to one of the triple thick sheets so it will not shift in transit. We leave about two inches around for protection to the edges. But, two triple thicks are pretty hard to dent.