tape machine logic puzzle

[turing]

hi, just picked up my very own tape machine, and it came bundled with a couple of reels of tape. now i may be being really dense here, but the tape is on the reel tails in, and oxide side out. i think there is some really obvious way of getting it off the reel and back on again so it's tails out oxide in, but i can't for the life of me work it out.
i tried flipping the reel round, and wound it onto the take up reel, but that just gave me the same problem. i suppose to those more used to dealing with tape it's a 2 second no brainer, so if anyone could enlighten it would be much appreciated.