I don't have a tanbur so haven't tried but I can think of two options. One is to put it in one of the various long hard cases that are used for skis,
golf clubs, and other sports things. Airlines go out of their way to cater to people who check these things. Much more important to them then
musicians are. Maybe one of these cases is long enough and wide enough at the base. The other option is to carry it on and store it upright in the
closet. Some will accept with a smile. Others will yell at you and forbid you to board. All depends.