Before flying I especially visited a GP to ask for something to help me sleep on the flight and she prescribed me some Zolpidem (apparently it's got a few names including Stilnox). I didn't find it very effective for me: the idea is that it's a pretty light medication that helps you sleep for eight hours and then you wake up without any woozy side-effects that you can get with the stronger meds. I took that on my flight up and I didn't find that I fell asleep immediately after taking it, or even grow noticeably tireder ... I was pretty tired anyway but couldn't sleep because of my relatively uncomfortable seating position (my head kept tipping forward as I fell asleep and that woke me up lol).
On the return trip I slept better thanks to the Dramamine that I took primarily for motion sickness but it also makes you drowsy. I was still fully functional in the airport, but I did find it helped me zone out a little easier lol.
In reality, between the inevitable jetlag you get on a long international flight (and I went 9 hours back in time to the West Coast of the US -> so I started waking up at 02:30 in the morning there), I don't think being sleepy is your biggest issue on the flight. It's more about getting comfy on the plane (and thank goodness Delta actually hands out face masks and ear plugs). I got one of those U-shaped neck pillows too, and combined with the blanket on the airplane and the extra room of the Comfort Plus seat on the return, I was all good
Some people on this thread recommended changing your watch to the new local time as soon as you get on the plane to help adjust to jetlag, but while that might help on a longer trip when your body can actually adjust I wouldn't recommend it on a shorter trip of a few days. Your body won't adjust quickly enough, so just sleep as much as you can whenever you can, because you will be waking up at very odd hours.
