I did the same as far as attaching a longbow tube to an arrow tube for air travel, but I actually glued the tubes together and didn't have tape on it while flying. They wouldn't allow tape because of conveyor belts or something. I forgot why.
I did have to use tape to hold the tubes together while the glue set of course. Here is how I made those tubes. I don't have a photo though as I gave those tubes to a friend years ago since I seldom fly.
To glue them, I got a 3rd tube that was SLIGHTLY shorter than the arrow tube and cut it LENGTHWISE into two halves by slicing it end to end. Once I did this, I cut a bit more off each half tube so I ended up with two pieces that were about 1/3rd of the sidewall of the original tube (looking at the end it was like a banana shape, but was about 30" long). I took one of these pieces and smeared PVC glue on the OUTER surface of it and then laid it between the other two tubes (with pipe sitting on the inner side of it to weight it down while it dried). Using this splice provided considerable glue surface to connect the two tubes.
After the glue dried, I flipped it over and glued the other 1/3rd on the other side so it would be strong and stable by doing the same as I did above. Once it dried, I removed the tape. The airline never complained about it being two packages as they were chemically joined together and made ONE unit.